Hey CptBuck, I saw this question when you posted it but haven't had a chance to tackle it. There's not a good overall study of prize money on the individual sailor's level that I know of, partly because it's super difficult to track individual sailors from ship to ship. They enlisted for a cruise, which is a vague term that could range from a few months to a few years, and when they were paid off at the end of the cruise they disappeared from ship's books. (That's another way to say that there was no such thing as e.g. a roster of enlisted men in the Navy or a fixed term of service -- that's a product of the mid- to late 19th century.) Most prize money accrued to captains and admirals -- before 1808, 1/8th of the value of a prize went to the admiral under whose orders the captain was sailing, 1/4 to the captain, 1/8 for the lieutenants, surgeon, master and Marine captain, 1/8 for the other warrant officers, and 1/4 to the crew. As you can see, that tends to distribute prize money to the top of the list, although the results were not inconsiderable to the common sailors either.
The captains most likely to find themselves awash in prize money were frigate captains who primarily cruised against merchant ships. To use a (non-representative) example, during the American war Captain J.S. Yorke took something like 56 prizes, of which we have accounts of 30, earning him at least £30,000 in prize money (his service pay was £146 per year). Four frigates that took the Spanish ships Thetis and Santa Brigida in 1799 shared in £652,000 of prize money; each ordinary seaman took home £182 4s 9 3/4d, which was the equivalent of ten years' pay, but the admiral cleared £81,000. Lord Howe caused a bit of a scandal when he retired to Bath while still in command of the Channel Fleet and continuing to receive prize money; but to be fair to him, he was elderly and his nerves broke after his squadron barely survived a violent southeasterly gale while anchored in Torbay, which is exposed from that quarter.
Now, in terms of investments, we know that sailors would sometimes use prize money or proceeds to start pubs -- this seems to have been a common dream of a seaman. We also have accounts of men simply using up their prize money on a binge on shore. There were usual investments available -- some captains urged their men to invest in Navy bonds or something with a fixed rate of return, such as Pitt's "Sinking Funds."
Now, as to buying a commission -- that would be impossible to do, simply because the Navy (unlike the Army) did not sell commissions; they had to be earned through sea-time and an examination. The idea of a gentleman having to prove his professional competency through an examination was socially revolutionary when it was required in 1677, and most likely came from the king, Charles II; it's doubtful Pepys (who gave himself credit for the idea) had anything like enough social standing to make a change of that magnitude. I wrote more about promotion in a few older threads: