95 Cavalier Transmission engage problems

When the car is put into gear (reverse or forward) you press the gas and it will act as if in neutral, then a second or two later will engage and slowly go. Eventually it will even shift gears while driving. Every stop I come to it starts over. Checked the fluid and it needs to be changed but what else might it be? I don't want to replace a tranny.

I know you said that it does this at every stop but does it do it mostly when it is cold and gets better when it's warm? I'd get a trandmission flush and change the filter. Try some Lucas with the new fluid as well. Stuff works miracles!