Spin the wheels and make sure they are reasonably true. Serious wobble side to side will mean the brakes will have to be spread wide and won't work well. Some play is inevitable on a used bike, however. While spinning the wheels feel/listen for the smoothness of the wheel bearings. Pull on the brake levers. They should move smoothly grab the rim well, and have some snap to them. That's not a deal breaker, though. Brake cables are cheap and easily replaced. I've not seen many used bikes that didn't need new brake cables. Check the tires for wear and cracked sidewalls. As with cables, tires are often shot on a used bike and aren't a deal breaker. I think I have some used 700C tires in serviceable shape if you need some.

Hold up the rear wheel, spin the pedals and shift the gears. It should shift easily without having to wrestle the lever. If it's stiff, that is still fixable. Look at the rear derailleur from the back, the cage and chain should be in line with the rear cogs, if it is bent, then you will have shifting problems, but you will be able to tell that from the racket it makes as you spin the drivetrain.
This is straight:


If it needs some work to get it roadworthy, I can help you with it on a weekend or evening sometime.