Power upgrades for Pontiac grand prix 08 base

Do you want a honest answer? Buy another car.

I wanted to but atm I'm just trying to build and have fun with my first car while in college. Planning on saving to get something nice once I graduate.

The cost of engine upgrades is quite expensive. Forget all you have heard about cold air intakes and loud mufflers which will do almost nothing at all. You could buy a V8 or a supercharged version of your car which would be a lot faster than the base 3.8 engine. Forget engine swaps as they are very costly and complicated.

Yea, I was thinking about saving up for a super charger and adding a ZZP 3800 1.0 PCM. I wanna go the more efficient way of upgrading because my car transmission went bad so I had to get a new one so I'm going to stick with it as long as I can.

Would a turbo be good? Also how much would that go for?

A turbo is much more complicated that supercharging. Do some searching and look for a GTP!