How to tell a cassette from a freewheel: http://www.sheldonbrown.com/free-k7.html

Friction shifting or indexed? If friction, I'd say just replace it with a 7-speed cassette freehub wheel. Then get yourself a 7-speed cassette and a new chain.

However, if you want to do this on a budget and re-use all your old parts, then go ahead and buy the wheelset you linked. I'm pretty confident you have a freewheel, but look through the above link to be sure.

One other thing: you need to know the spacing of your frame: http://www.sheldonbrown.com/gloss_sp-ss.html#spacing This is very easy to measure. If your frame is steel you can bend it to accommodate a wider wheel, but you won't be able to bend it from, say, 126mm to 135mm. Your option then is to re-space the rear wheel and cut the axle short.