It has a 4L60-E in it right now. If you don't like electronic units (so easy to program!) you can swap in a 700R4 pretty easily. My buddy Mark runs a built 700R4 in his 87 LT1-powered Iroc drag car.
Of course, I later got a C5 and the current Trans Am and converted to T56. So I'd likely drop a T-56 in the RS if I were keeping it. That, too, is dirt simple. Get pedals and cylinder off another 3rd gen (I've heard you can use 4th gen parts for this, but not sure) then get a T56 from a 4th gen. Purchase a crossmember from Andris Skulte at Skulte Performance (Fellow CTFBA member) cut the square for the shifter and go to town. Swap itself doesn't cost much, essentially just the cost of the transmission unless you want to simultaneously add a SPEC Stage 3 carbon ceramic clutch and Fidanza 11lb lightweight flywheel like I would....