You're likely looking for a trailerable sailboat.

You won't get a powerboat of sufficient size, in any kind of condition at all,
for the amount you're budgeting- particularly since
extreme fuel efficiency is important.

If you want to cruise for several weeks at a time, you'll need some room aboard
for stowage and comfort.

At $15k, you're looking at maybe a 20- year old, 25-foot powerboat with
(typically) a big block gas engine and needing some serious repairs.

If you can find a trailerable sailboat, it will be powered with a small
outboard or, if you're lucky, with a small diesel perhaps replacing the
original Atomic 4.

Sailboats are less beamy than powerboats, and you might get into a longer boat
before you run afoul of the wide-load restrictions.

Besides, darn few sailors ever succesfully tansit to a powerboat- other than a
trawler.
Trailerable diesel trawler for $15k? Certainly not a commonly available
critter.