To be faster-
Add power and loose weight.
On a budget:
To add power-
Add cold air intake
Add cat back exhaust
To loose weight-
Go with lightweight wheels/rims doesn't really matter what size but 15" is probably the best balance of performance with lower weight and lower price but still good selection of styles. 14" also possible if budget is limited.
Get sticky rubber to go with the rims- ultra high performance summer tires if your weather allows or maybe ultra high performance all season tires if you get some light snow.
To round out your performance:
Improve suspension-
Lowering springs or upgrade shocks
To make the most out of your upgrades-
Send the nut behind the wheel to driving school at least once a year.
Practice driving at autocross or at the track- seek an instructor when possible and give yourself time to learn. If it was easy to drive well we would all be like Mario Andretti.