Trans Am's most definately came with a four speed manual box in them. It's the exact same one used in the Chevy and GMC trucks, Camaro, Corvette, etc. All the RWD V-8's use the same stick tranny.
The Firebirds and R/S versions of the T/A also had the option of a 5 speed, but they weren't too popular, so are extremely rare to find.
If you find a T/A with a 305 in it, walk away. The 305 is basically a castrated 350 with cylinder sleeves, which destroy the power, fuel mileage, and reliability of the venerable 350. I should know, it's the exact engine that's in my truck. Balls amounts of torque, but my Yoda will almost out accelerate it. And my truck only gets 10-12mpg. One of my coworkers has the exact same truck, but with a 350 in it, he can leave two smoking black trails of rubber for YARDS down the road, bouncing your head off the rear window of the cab, and he's pushed it over 20mpg driving it like a granny. He normally gets 17-18mpg out of it.
If you find a Firebird or a T/A with a 350, 327, or the even more prized 454, snatch it up. They are a bulletproof engine. The 700 series tranny is also bulletproof. And I'll agree that the 350 series tranny sucks danglies. Again, I know. Again, it's the one that's in my truck. So far I've been lucky and not needed to coax mine along at all, but I know the day can't be that far away where I'll be plonking a 700 series into it with a 350CID V-8 attatched to it.