One of my scopes is a GW GOS-522 20MHz scope, I bought it second hand, I've found it quite a decent little scope!.
Anyway, Z input - this is simply a brightness modulation input, so X is left to right, Y is up and down, Z is 'backwards and forwards'. Generally you need a high signal level to modulate it (spec on mine says 3V p-p, 50V max), but personally I've never had occasion to use it either at home, or at work.
One nice feature on mine (I don't know if your's has it?) is an output on the back from CH1, this allows you to connect a frequency counter after the preamp in the scope.