Plan on getting a hardtail unless you're planning on spending close to $1k or more. I'd shoot for a decent-quality 5-year-old major brand hardtail in the $100-200 range, then plan on fixing it up with at least Koolstop salmon pads for the V-brakes (discs are welcome but less likely in this price range), and probably a new chain and rear cassette. You may also have to buy new wheels (a decent shimano xt/DT/Rhynolite wheelset usable with either V brakes or discs can be had for $160 or so). A new set of decent off-road tires will run you $50 if you shop wisely.

Problems that are hard/expensive to fix: bent/cracked frames, worn-out front shock.

Use bikepedia.com to look up the specs/price/components of specific model/year of bikes you are interested in, and remember that bike value instantly drops to 1/2 of MSRP once it leaves the dealer, and keeps dropping rapidly after that.