Sounds like a logical route to go. You can replace the rear wheel without worrying about the front. Freewheel with 7 speed cassette is fine and allows you to keep your existing shifters. Definately replace the cable (do them all while you are at it) and clean and lube the BB bearings (and do the front hubs as well). Building your own wheel is doable but I'd suggest buying one to get yourself on the road and concentrate on the other do-it-yourself projects the bike needs.