I dont have a civic, but I have done a range of performance mods to my car (a 99 Supercharged Grand Prix...sort of an anti-civic 🙂 ). Anyway, you'd need to do some research, but for handling there are a few inexpensive mods that you can typically do. Front and rear strut tower bars are usually pretty cheap and easy to install and help keep the body a little flatter in hard turns. Also, sway bars again help with body roll, but they are a little harder to install (but still possible with instructions and the right tools).
DONT get a wing...
If you want to add power, you can always look into NOS. Just dont get a ghey fogger like in Fast and the Furious. Also, get one that kicks in at wide open throttle not via a big red button (again like Fast and the Furious). Trouble with NOS is that it can be dangerous. I think a small 35HP shot or so would be pretty safe, but do this at your own risk. I also would assume that a new intake would help a little bit as would exhaust, but stay away from the fart can/can of angry bees mufflers.