What affordable "type" is best for longterm cruising?
There is a big difference between living aboard and long range cruising and there is also a very big difference in the requirements for both. The cheapest and most comfortable way to live aboard, assuming that you don''t care about sailing or going anywhere is to buy an old houseboat with blown engines and just park it somewhere. If you really want to go somewhere, then you give up a lot of room and potentially add a lot of cost. It will be extremely hard to find a suitable live aboard with decent accomodations and good sailing ability in ready to go condition, for anything like $15K. Anything in that price range will be a compromise. That said, you are young and fit, and so probably can live with some degree of compromise.
In your price range you are probably looking at a roughly 28 to 32 foot sailboat from the 1960''s or 1970''s, probably with a gas engine. It will probably need a lot of work to make it capable of cruising the Islands but some of this can be done over time. I doubt you will find a decently constructed catamarran in that price range.