One of the main purposes of your first bike is helping you understand what you want your second bike to be. That's not to say you won't like your first bike, but the more you ride, the more you'll know what you really want, so it makes sense to go cheap at this point and think about resale value.

The bike I'd recommend is a late 80's or early 90's mountain bike with a rigid front fork. These bikes are plentiful in the used market, sell for around $100 and are generally very tough. The best part is that you can buy one of these and ride it for two years and then sell it for around the same price you paid for it. Look for something from Specialized, Trek or Giant. I'm particularly partial to Specialized Rockhoppers. There are some other brands that will be as good, but these are the most common so sticking with them simplifies your search.

As for evaluating a used bike, this is a general procedure: Look at the bike to make sure it doesn't have any significant rust on the frame or the moving parts. Lift the front wheel and make sure the handlebars turn smoothly back and forth. Give it a shake to see if anything is loose. Lean on it a bit side to side to see if anything creaks. Spin front and back wheels to make sure they spin freely and don't wobble. The front wheel should keep spinning for around a minute before it stops. Finally, take the bike for a ride. Start by adjusting the seat height until you can barely touch the ground. Make sure the bike is comfortable for you. Give the brakes a try before you go far. Make sure the brakes work well and the shifting is functional for all gears. Don't worry too much about the condition of the tires, as you'll probably want to replace them anyway (especially if they're knobby). Replacing the brake pads is pretty cheap and usually worth doing. Everything else should be in ready-to-ride condition. If the bike passes all these tests, you should be OK.