On a 30 foot sailboat in the $5k range, I wouldn't be amazingly concerned about the bottom. It's going to be old, with uneven paint, blisters, scrapes. The bottom is not going to give out- it's solid glass. Usually. A bad bottom is an issue with a racer, but not really for a new sailor on a tight budget...unless it's unbelievably bad, then of course you can probably find a better one.
The bigger worries are the engine and its ancillaries IE: trans, shaft, tank, etc., the sail rig, and the keel. Don't fret over moisture in the decks on a 5k boat, unless your rig is attached to it IE: bulkhead mounted chainplates.
If it floats, the motor runs and drives, the rig is safe and usable, and the keel and rudder aren't going to fall off, those are your primary concerns. I'd also peak at the wiring, anywhere you can find it.
You don't want fire, hull breach, keel or rig failure. Anything else that breaks will be less than catastrophic.
I would seriously look at a Catalina 27 - 70's vintage. Solid boats, easy to work on, easy to sail. And cheap. I'll wager you can find one in your price, or even lower. An outboard version might be the simplest; a diesel will command more $.
Regarding headroom, the 27 is not bad - you will still need to stoop. However, much of your time will be spent in the cockpit. Even in the cabin you're usually sitting or laying down anyway. It won't be fabulous, but you'll get used to the low roof.
In a 30, you might look at an old Pearson or Bristol 30. Bulletproof builds, and usually restorable, if that's something you want to eventually do.
Sorry if I've repeated anyone - I didn't read the whole thread
Good luck.
Edit: This is an example of exacly what I'm referring to in a Catalina 27:
http://www.sailboatlistings.com/view/42527