Although MacMillan gives the part of speech for plenty as either pronoun or adverb, depending on usage, other dictionaries are careful to specify that in the case of plenty of + noun object(s), it is a quantifier (or noun?). From the Collins English Dictionary:
If there is plenty of something, there is a large amount of it. If there are plenty of things, there are many of them.
Ex. There are plenty of cars on display here.
Notice that the number of the verb is plural to agree with the number of the noun object. By way of contrast...
Ex. There was still plenty of time to take Jill out for pizza.
Once again, the verb agrees with the non-count noun "time".
Since there are several disparate (as Edwin Ashworth refers to them) items on your list, they should be considered as plural. i.e. You would say plenty of them, or those items, and not plenty of that; even though each one taken by itself would be a non-count noun taking singular agreement of the verb.
Random House Kernerman Webster´s College Dictionary agrees with Collins in this, but also says:
usage: The construction PLENTY OF is standard in all varieties of speech and writing: plenty of room in the shed.
The use of PLENTY preceding a noun, without an intervening OF , first appeared in the late 19th century: plenty room in the shed. It occurs today chiefly in informal speech.
So, in your sentence we would have;
Plenty of time, space, and money are needed
[Even though, somehow, someway, is sounds better to my ear. Go figure.]