What do I need to know about fitting new wheels on a bike? My girlfriend has had the wheels stolen from her bike. I'd like to replace them, but we're working with a limited budget so I'm going to do the work myself and source the parts second hand.

I've done a basic bike maintenance course but beyond that I'm relatively clueless. I know that the new wheels need to be 700C's, and that the new rear gear cassette needs to be 7-speed (I guess because that's what the gear shifters are) but I have the following questions:


Will any 700C wheel work with any gear cassette? From browsing eBay it seems that some of the wheels are specified as working with 7-speed or 8-speed cassettes?
The first question aside, will any cassette screw on to the mounting on the wheel I buy, or are there different threads?
Should I buy a free wheel or a cassette? I'm not even sure what the difference is!
There are a number of factors to consider when buying a new wheel set:


Wheel size, there are many different wheel sizes to choose from, modern road bikes are generally 700c and mountain bikes 26, 27.5 or 29inch. There's also a number of legacy, children's and specialty sizes.
Rim width, rim width determines how wide a tire you can run and is determined by seat stay and chain stay clearance. If you have a road bike you may be able to fit wider cross tires if you were so inclined.
Axle width, the width of the rear drop outs, generally 135mm on road bikes but older bikes may be less, 135 or 142 for mountain bikes. Front widths on mountain bikes are either 100 or 110.
Cassette size, you need a hub (unless using a free wheel) that is spaced for the cassette you'll be using. There are 7, 8/9/10 and 11 speed free hubs. A 7 speed cassette will fit an 8 speed hub with a spacer.
Cassette type, shimano and sram require a compatible hub, campy requires a different compatible hub.
Brake type, rim brakes need a specific rim, disc brakes and coaster brakes require a specific hub.
Axle diameter, on Mountain bikes there's 9mm QR and 15mm and 20mm thru axle on the front and 10mm QR, 10mm bolt up or 12mm thru axle on the rear.


Everything thing else such as material, number of spokes or valve type is user preference.