It seems the OED missed the mark for the origin of this phrase by decades. (This is a pattern I have noticed; for phrases in particular a Google Books search often returns earlier examples than the OED.)
All evidence points to the origin being medical. The earliest example I can find of "drug(s) of choice" is 1909 (bold mine):
On the other hand, there are a number of conditions in which the known physiologic action of ether makes it distinctly the drug of choice.
Again, given a case of nephritis, new or old, chloroform is the drug of choice in most instances because, although quantity for quantity it is far more irritating to the kidneys than ether[...]
Surgery, Its Principles and Practice: Vascular; gynecology; anesthesia; x-rays; operative & plastic; infections; legal pathologic relations; hospital organization
I found several other early examples of the phrase using Google Books, but this one is the earliest (note that some of the results are incorrectly dated).
However, there are similar expressions that predate this one, with many examples found in this source from 1897 (bold mine):
A paper on this subject appears in the February number of The Post-Graduate, by Dr. G. M. Edebohls, which gives the following conclusions:
"The classical operation from below Poupart's ligament should be the operation of choice for femoral hernia, the inguinal operation being performed only upon special indications."
In one instance, Case I., ether should have been the anaesthetic of choice, and in Case II. chloroform would undoubtedly have been the better anaesthetic.
"3. In the majority of gall stone cases, causing obstruction of the common duct, there are also stones in the cystic duct and gall bladder, then cholecystostomy should be the operation of choice"*
Pyloroplasty is the operation of choice.
"It is the method of choice in almost every case; but there are a very few cases, such as that just reported."*
The Post-Graduate Journal for August, 1897, contains a valuable article on this subject, by Eugene Fuller, M.D., New York. He says:
"Litholapaxy causes no mutilation, and in the hands of a skilled operator it is at tended with less danger than a cutting operation. Consequently it should be the procedure of choice over any form of cutting operation, if it is capable of accomplishing a radical cure."
Medical Review of Reviews, Volume 3
* It's not clear for either of these quotes what exactly is being quoted.
An even earlier source comes from 1896 (bold mine):
Gastrostomy is the operation of choice in impermeable cancerous strictures.
When the large bowel is the viscus involved, the conditions are reversed, and the fixation of the gut-end in the wound after resection of the gangrenous portion becomes the operation of choice.
Again, when the location of the obstruction is such that an anastomosis between comparatively distant parts of the intestine is the operation of choice for its relief, a median abdominal incision would be required, as, for example, when right inguinal colotomy has been done for the relief of obstruction at the hepatic flexure of the colon, and an anastornosis between the transverse colon and the ileum is required, or, on the other side, an anastomosis between the transverse colon and the sigmoid flexure is desirable for the relief of an obstruction in the descending colon or beginning of the sigmoid for which an opening in the loin or left inguinal region has been made.
When the mobility of the affected portion of the bowel is such as to prevent adossement being used without any strain upon any part of the suture line, it is the method of choice.
Lateral anastomosis therefore remains as the procedure of choice in the cases under consideration when adossement is impracticable.
The latter is the method of choice, as being possible of accomplishment with comparative speed and case, while it restores the natural relation of the small to the large intestine.
For these reasons the lumbar route has ceased to be the method of choice, except, possibly, in cases in which by prolonged obstruction the distention of the colon has become extreme and its immediate opening is imperative.
System of Surgery: Tumors, hernia, surgery of the alimentary canal, appendicitis, surgery of the liver and biliary passages, of the uterus, of the ovaries and tubes, gynecological surgery, symphysiotomy, surgery of the thyroid, surgical peculiarities of the negro, surgery of the female breast, use of the röntgen rays in surgery
Given the fact that there are so many examples in two sources published so close together, it is likely that there are earlier relevant attestations of "X of choice" that I have not found.