1. The pool experience I have is with the pump running 24/7. Does yours only run at certain times - or on for a period and off for a period?
2. As for the pump itself, you don't want to get just any pump... you want to be sure to get one that is designed for the volume of your pool. Check with a local pool supply co. to confirm what's recommended for your pool.
3. GFCI is a designation of the outlet, not the pump. The pool-pump I last dealt with was plugged into a regular outlet, not GFCI... but I'm not positive if this is considered correct... you might ask the local pool guy this question too. If he says it needs plugged into a GFCI outlet, then that's easy. The outlet will cost you about $10 and anyone with a screwdriver can install it.
Hope that at least helps a little...