The first mod i did on my 997 turbo was the DSC box, that transformed the handling. Then I fitted Michelin PS4S tyres, a GT2RS rear anti-roll bar as they are cheap and had Centre Gravity set the handling up. The difference in handling was now staggering. The tyres gave so much grip, even in the wet and you could actually "feel" the road. The GT2RS roll bar tightened up the turn in.
Once I got the car handling well, I eventually did the performance mods. If you are on a budget, the GT2RS intercoolers are cheap and pretty much bolt on - theres plenty of guides online showing how to fit them. This plus an exhaust, air filter, uprated clutch (if yours is a manual) & a remap will get you a nice power boost. If moneys not so tight, then you could go for the do88 big pack, do88 plendum, gt3 throttle body and get even more power.
One thing to remember though, these gen1 car are getting old now, so before you start modding id have the car thoroughly inspected and replace any bits which are worn or needing replacement. I did that before I did the performance mods and there was quite a few grand to spend to bring it up to scratch. All stuff which didnt really affect the running of the car but would have caused issues before long.
Oh, and a quick shifter is another good cheap mod to do!