I'm in a similar situation.

I'm a graduating college in May and want to go trans-America before starting work in August. I'm pretty low on cash so I want to keep my bike expenses as low as I can. I am in Pittsburgh so I have access to my local bike coop, Free Ride, which has bins of old parts and some new things for good prices. It also has older mountain bikes coming through from time to time.

I also have a few bikes and parts, none of which are terribly well-suited for the job at hand:
-a Univega Alpina Pro with mostly 1990ish Deore parts, but which I have ridden through winter and thus with a bit of corrosion on some parts. It's also a bit too small on me.
-a busted (broken frame) Diamondback ~1990ish bike with some Deore XT parts on it
-a set of touring wheels built on Record hubs with a 6speed Suntour freewheel
-various other parts

I guess my big questions are, for reliability's sake, what's worth buying new, and where do old parts do fine? It seems to be best to have a new drivetrain and wheels, since those are where a lot of force goes through and would be bad news trying to hack together a fix for deep into the Great Plains. Used frames, brakes, bars, stems, and so on seem fine though. Is that reasonable?