1992 Buick Lesabre transmission or fuel pump?

Transmission problem
1992 Buick Lesabre 6 cyl Front Wheel Drive Automatic

ok I bought a 1992 buick lesabre custom for 400 a couple days ago. The people we bought it from claimed the fuel pump was bad and they said go easy on the gas pedal because if you press to hard it won't go anywhere and on hills it really won't work. So when this happens the car stays on and just revs but won't move. We got it home ok but had to give it a little push on a hill but other than that we were just going kind of slow but on the interstate it was perfect. So today my dad drove it and tells me the transmission works intermittenly and won't slip into gear. I really need an answer! Plz help