In general, avoid anything needing serious work unless you are a competent home mechanic. I recommend buying an inexpensive chain tool to bring along--avoid anything with a significantly worn chain as the cost of replacing the chain, cassette, and possibly chainrings is going to seriously effect how much money you'll need to put into the bike. I would avoid anything with suspension components more than two years old in general unless the bike has seen very low mileage and/or the owner can explain that the suspension has been frequently and professionally serviced. Also avoid mountain bikes that look like they've been ridden hard, even for a season or two. If you're not used to assessing bikes, I'd steer you away from carbon mostly and definitely from any carbon that looks like it has many or hard miles.
Basically: check the chain, avoid stuff that's clearly seen a lot of use unless you know what you're doing, be wary of how some mountain bikers can destroy their bikes in a few seasons.