I have a 2008 Acura Tl Type-S and I want to get a straight pipe. Which size pipe would help gain instead of lose performance?

The size of the pipe isn't going to get you more power on an engine that small. Sorry to break it to ya. Only way a bigger pipe would help would be if the original was too small and restrictive. Which is very unlikely. I'll put it this way, I have a 385 horsepower 5.0 V8, and it's exhausted with a 2.75" pipe. If that's big enough for an engine this big, anything bigger than 2 inches is plenty for your Acura.

I plan to keep the cat

The straight pipe is not only illegal but will cause the car to run worse. The cars computer is programmed for optimal performance with the system as manufactured. Take away the cat and the back pressure and the computer will go bananas.

Straight Pipes are unlawful in every state and DC.

When caught you will have to replace the system completely.

Any Auto Parts store should help you.

Less compression would give a little better performance IF the computer is programed for it. The noise (no muffler, no catalytic converter) will attract the coppers.