Are there any accounts of common sailors/seamen, press-ganged or otherwise, buying a commission, perhaps with prize money? Is Master the best one could hope for?
The short answer to this is "no" because, at least in Britain, RN commissions were neither bought nor sold, but earned via years of service and upon passing an entrance examination that would create someone as a lieutenant. This was fundamentally different from service in the Army, and fairly revolutionary -- although Samuel Pepys gives himself credit for this, as he does with many things, it's fairly clear that Charles II would have had to be behind the notion that gentlemen would have to be professionally examined to be able to "pass" for lieutenant's rank and later.
A master's rank was in any case that of a warrant officer, not a commissioned officer -- I'll drop in some links momentarily -- but only pursers, who were entrusted with payrolls, had to put up sureties (or bonds) for their position starting in the mid-17th century. And they were also warrant officers. The rank of "master" is slightly confusing, because there was also a rank of "master and commander" as a commissioned officer, but that rank was meant to confer command of a ship upon a deserving lieutenant before offering them a rank of "post-captain," which would set a man upon an inevitable ladder of seniority that would end in an admiral's rank or their death, whichever came first.
So there was no such thing as "buying" a commission in the RN. However, the merit-based nature of the job meant that the outstanding admiral of the age was one of eleven children of a Norfolk country parson.
Some more on becoming an officer, and promotion and so forth, here:
and
and on impressment here:
https://www.reddit.com/r/AskHistorians/comments/2oo91z/during_the_age_of_sail_how_reliable_were/
Hope this helps, let me know if you have follow-up questions!