Early versions of the proverbial phrase
According to Martin Manser, The Facts on File Dictionary of Proverbs (2002) has this entry for the proverb in question:
a jack of all trades is master of none
Somebody who has a very wide range of abilities or skills usually does not excel at any of them: We encourage our students to specialize at an early age, on the basis that a jack of all trades is master of none. The proverb was first recorded in 1732 in the form "A jack of all trades is of no trade." It is perhaps most frequently encountered in the form of the cliche a jack of all trades.
Manser's 1732 source is evidently Thomas Fuller, Gnomologia: Adagies and Proverbs; Wise Sentences and Witty Sayings, Ancient and Modern, Foreign and British (1732), which offers this bare-bones adage as number 3051 in his collection, sandwiched between "Jack in an Office, is a great Man" and "Jack would be a Gentleman, if he could but speak French":
Jack of all Trades is of no Trade.
The same book also has this entry (at number 304):
A Man of Many Trades begs his Bread on Sundays.
The phrase "Jack of all trades" is, of course, much older than that. The earliest instance that a search for the phrase (with or without hyphens) at Early English Books Online turns up is from John Cleveland, "Smectymnuus, or the Club-Divines," in The Character of a London-Diurnall with Severall Select Poems (1647):
The Saints Monopolie, the zealous Cluster, / Which like a Porcupine presents a Muster, / And shoots his quills at Bishops and their Sees, / A devout litter of young Maccabees. / Thus Jack-of-all-trades hath devoutly showne, / The twelve Apostles on a Cherry-stone.
And from a 1654 translation of Charles Sorel, The Extravagant Shepherd, or, The History of the Shepherd Lysis, an Anti-Romance:
For Homers sentences, besides that they are such as it may be were in every mouth in those days, all sects of Philosophy have gotten somewhat out of him ; as if he commend Vertue, he is presently a Stoick, &c. Nor have they been more fortunate, that make him Master of all Arts; or to say better, a Jack of all Trades. For to make him a Ship-Carpenter, 'tis enough that he makes his Ulisses one : To shew that he was a good Cook, he made his Hero turn the spit, and boil the pot, and in Vulcan he is an Armourer : This was an easie way to be of all Trades ; but it is to be thought, that Ignorance and Pedantry were the Godfathers that gave him that name.
G.L. Apperson, English Proverbs and Proverbial Phrases (1929), cites two even earlier relevant instances, from 1618 and 1639:
Jack of all trades. 1618: Minshull, Essayes, etc., 50 (1821), Some broken citizen who hath plaid Jack-of-all-trades. 1639: Mayne, City Match. II,v. Why you mongrel. You John-of-all-trades.
The first quotation that Apperson cites is from Geffray Mynshul, Essayes and Characters of a Prison and Prisoners (1618):
Now for the most part your porter is either some broken cittizen, who hath plaid Jack-of-all-trades, some pander, broker, or hangman, that hath plaid the knaue with all men, and for the more certainty his embleme is a red beard, to which sacke hath made his nose cousin german.
The second quotation is from Jasper Maine, The City-Match (1639):
Quartfield [a captain]. Why, you mungrel, / You John of all Trades, have we been your guests / Since you first kept a tavern ; when you had / The face and impudence to hang a bush / Out to three pints of claret, two of sack, / In all the World?
James Burgh, The Art of Speaking, fifth edition (1761) offers a variant on the "master of none" theme, quoting a translation of a dialogue by Lucian:
7th Ghost. Sir I am an universal genius.
Merc[ury]. That is to say, in plain English, a Jack of all trades, and good at none.
Instances of this version of the expression go back to at least 1721, according to Bartlett Whiting, Early American Proverbs and Proverbial Phrases (1977):
A Jack of all trades and good at none (varied) [First two cited examples:] 1721 Boston News-Letter in Buckingham Specimens 1.8: Jack of all Trades, and it would seem, Good at none. 1723 New-England Courant 100(2.1): They can, like Children, play Jack of all Trades, tho' they understand none.
Finally, the form "jack of all trades but master of none" is approximately expressed in Charles Lucas, "Pharmacomastix: or, The Office, Use and Abuse of Apothecaries Explained, &c." (1741), reprinted in The Political Works of C. Lucas, volume 1 (1785):
The very Druggist, who in all other nations in Europe in but a Pharmacopola, a mere drug-merchant, a mere drug-merchant, is with us, not only a physician and chirurgeon, but also a Galenic and Cbemic apothecary ; a seller of druggs, medicines, vertices, oils, paints or colours poysons, &c. a Jack of all trades, and in truth, master of none——For bad as the usual education of an apothecary may be, if it could be yet worse, he may make a good modern druggist enough.
And again, from a letter to the editor of The Town and Country Magazine, Or, Universal Repository of Knowledge, Instruction, and Entertainment (March 1785):
In a rude state every man is obliged to provide for himself, with his own hands, whatever he stands in need of, without having recourse to the assistance of others. He is his own taylor, his own shoemaker, his own carpenter, his own builder, &c. in a word, he is his own general tradesman ; or, to use a very common, but, at the same time, a very significant expression, he is a Jack of all trades, but master of none: whereas, in a civilized state, all these different trades, and a vast variety of others, are confined to particular classes of people : nay, each particular trade is divided into a number of subordinate branches, each of which, in its turn, is likewise performed by a certain set of men ; the consequence of which is, that every commodity, of whatever kind, is not only produced in much higher perfection, but likewise in much greater abundance, than it could possibly be otherwise.
Variants that are relative newcomers
As for the suggested longer expression "Jack of all trades, master of none, but better than a master of one," the earliest matches I could find for it are two instances from 2007. From Drum magazine (2007) [combined snippets]:
The full phrase is actually "Jack of all trades, master of none, though ofttimes better than master of one". Being multi-skilled prepares you to be a more dynamic, flexible worker. If you are looking to grow beyond your job and become a general manager or CEO, then you must be prepared to get out of your departmental comfort zone and learn about the processes in other departments.
And from Principal magazine (2007):
All of these roles don't even take into account the principal's job as a traffic control officer, safety inspector, instructional technology specialist, dietician, health-care provider, and inventory-control manager. As the saying goes: "Jack of all trades, master of none, though ofttimes better than master of one." But principals cannot afford to be master of none because every child in school depends on you to be master of all of these roles.
The expression also appears in Todd Grossman, Shooting Action Sports: The Ultimate Guide to Extreme Filmmaking (2008):
Jack-of-All-Trades, Master of None
We've all heard that expression, but what we rarely hear is the end of it. The original complete epithet reads: "Jack-of-all-trades, master of none, though oftentimes better than master of one." Interestingly enough, the world is changing to a more complicated, more integrated place. The latter version of the saying, in its totality, puts the emphasis back on the benefit of being good at many things.
And in Jonathan Cook, The Work of the Bursar: A Jack of All Trades?: Essays in Leadership for Changing Times (2011):
Furthermore if,We hope, too, that the book's sub-title Jack of all trades? causes no raised eyebrows. In terms of gender, yes: these days there are many Jills, as well as Jacks, occupying in the bursar's chair. Furthermore if, when one hears the phrase, one often thinks of the words which tend immediately to follow it: 'Master of none', it is worth remembering the saying in fullest version: 'Jack of all trades, Master of none; though oftentimes better than master of one'. Bursars truly are practitioners of many parts.
And in Mark Forshaw, "Writing, Training, Teaching, Researching, Consulting, Quality Assurance and the Kitchen Sink," (2013), in Mark Forshaw & David Sheffield, Health Psychology in Action (2013):
What is good is to have a sense of worth derived from being someone who does a bit of everything. I am a jack of all trades. Perhaps that means I am a master of none, as the figure of speech goes. If so, then so be it. I won't be known as the world expert on something or other, but I might be useful at times. Knowing a bit about everything has its moments. What people often don't know is the full version of the phrase: 'Jack of all trades, master of none, though ofttimes better than master of one'. In Dutch, I would be a manusje van alles, and that's more often than not a very positive phrase.
And in Tiisetso Maloma, The Anxious Entrepreneur: Anxiety Defeats Creativity | Creativity Defeats Anxiety (2016):
By the way, not to make a point but to just put it out there, the quote, "jack of all trades, master of none", doesn't end there; the last clause in it was conveniently lot. I guess, to suit the opposite context.
In full it says; “Jack of all trades, master of none, though oft times better than master of one”.
Several of these excerpts make a point of claiming that the extra-long version is the original wording. But it seems more likely that the extra-long version was a very recent formulation, perhaps influenced by the memory of a concerted effort by educators in 1930 to alter the old adage to suit a new objective. A Google Books search finds a gaggle of four matches in 1930 for the phrase "a student of all arts and a master of one" in periodicals devoted to education. Three of the pieces—which appear in The Nation's Schools, Educational Administration & Supervision, and the Association for Student Teaching Yearbook—appear to be identical:
For surely, in this day and age, few, if any, school administrators will be content with teachers who are, in the one case, narrow unsympathetic specialists, or who are, in the other case, Jacks-of-all-trades an masters of none. For administrators know that the teacher who is interested in his own specialty only is not in fact a real master of that specialty. Mastery connotes understanding a thing both when it is abstracted and isolated and when it is combined and related to other things.
These two types of training in combination—liberal culture and vocational culture—produce professional equipment which, at its best, signifies an appreciation of many branches of learning and a mastery of one of them. It is thus the conversion of the old adage from "A Jack of all trades and a master of none" into "A student of all arts and a master of one."
The Michigan Education Journal (1930) has a slightly different presentation of the same campaign:
The other seeks to equip the teacher with a body of specialized knowledge, to make him familiar with the laws and forms which explain that knowledge, and to train him to become a fair master of the tools and processes by which he may interpret and present that knowledge to others who are more or less ignorant of it. The combined aim is to convert the old adage from 'a Jack of all trades and a master of none' into 'a Jack of all trades and a master of one.'
The educational rewrite of the old proverbial phrase survived into the 1950s in such outlets as Mosquito News (1951) and All Hands magazine (1956). And inevitably, someone—in this case, Chuck Missler, How to Study the Bible (2017)—had to announce not only that "jack of all trades and a master of none was a mangling of the original "jack of all trades and master of one," but also that the originator of the correct expression was Ben Franklin.
To sum up, I offer this timeline of the earliest occurrences I could find for the various forms of jack of all trades and the proverbial phrases built up around it:
1721 Jack of all trades, and it would seem, Good at none
1732 Jack of all Trades is of no Trade
1741 Jack of all trades, and in truth, master of none
1785 a Jack of all trades, but master of none
1930 a Jack of all trades and a master of one
2007 Jack of all trades, master of none, though ofttimes better than master of one
The extra-long version of the expression may be considerably older than the 2007 earliest established occurrence might suggest—perhaps even a decade or two older. But it isn't the original form of the expression; and in comparison with the forms that arose during the 1700s, it is quite young.