Welcome to the forum...
You can certainly find a boat in your price range, it's a bit of a buyers market these days and so if you know what you want, and what to look for/avoid you should do OK. Have you investigated the liveaboard option completely? It may not be as inexpensive as you imagine, even assuming you can arrange for moorage with legal liveaboard status.
You should be able to line up a relatively good Catalina 30, maybe even an early Cat 34 if you get lucky... either would be a good single's liveaboard.. But really you need to find the best boat you can afford, make aside, allowing for the known problem boats.
Sit down and formulate a list... things you need, things you like, things you can do without.. Cabin heat, dodger, cockpit enclosure, large berths, headroom, (how tall are you?) Wheel vs tiller, gas vs diesel, stove type, good performance under sail, good performance & maneuverability under power, storage capacity, fuel and water capacity etc etc.
If you're an inexperienced boater the problem will be even knowing what you need to want.. or what to look for. Is this going to be essentially a floating condo or do you plan to cast off the lines frequently?
Sounds like you like the heavier, full keel concept - that will rule out some of the items above. Your budget rules out IP but keep an eye out for some Bayfield 29s or 32s, similar concept and more affordable. Other boats like older Cape Dorys, Albergs, etc will fit the bill too but will tend to have less interior volume.
Craigslist is a viable way to buy, esp today, but you do need to know enough to eliminate the ones that aren't worth surveying and you'll need to do more travelling and running around than making the brokerage rounds.
I'd suggest doing the brokerage tour as an education exercise.. find out what appeals to you and then start searching out similar boats in other venues like CL.
Here's a Yachtworld search in your immediate area, with your budget specs:
(lots of big wooden boats early on... don't get too excited about those... wood is a lot of work and big is a lot of expense after the fact.)