What you want to do is write down the numbers on the side of the tire. They'll be something like P215/60R16. This is the magic number you'll want to talk to tire dealers quickly. That number tells them a) the tire diameter b)the rim width and c)the aspect ratio (sidewall height to rim width). A more detailed explanation is here.

What more money buys you in tires is usually better traction, better tread life or a quieter ride (not usually all three in one tire, you have to make tradeoffs).

The two most important thing you can do to make sure your tires last are: check your tire pressure frequently and keep your car well aligned. That and don't hit a nail.

Of course you'll have to take into account whether you want a dedicated summer/rain tire or if you want an all-season radial.

-Zeke