The above is excellent advice.
I think i'd "upgrade" to a 9speed, not because it's actually better, but because you'll more easily find quality replacement items in 9speed than in 7speed. Of course, this is assuming you have a freehub set-up, not a freewheel.
Also, if your shifters are ancient enough, and they run on friction, they'll almost certainly have enough pull to run across a 9speed cassette. If they're indexed, then you'll need a new rear shifter, as dude with the Ryu avatar had mentioned. Shifters are expensive.