Faster "in a straight line" will take some considerable cash investment if you are looking for anything really noticeable e.g. Turbocharger or supercharger.
I personally settled for faster "around the twisty bits" and focused on suspension and stiffening the chassis. I will shortly be getting better brakes too (I like to stop 'fast' too!).
There are some nice body kits around; I saw a decent looking one being promoted on 9thgencorolla.com which looks slick and durable.
If you want to go faster without investing a lot you could go:
CAI
PPE headers and midpipe
Magnaflow back section
Emanage
then rip out the back seats; the spare wheel and jack and anything else that adds weight. Swap out the stock wheels for something in the 14lbs range.
Oops; did I say 'not investing a lot"?
I hope this helps a bit and remember, at the end of the day it is your car and your money and you should do what makes you happy.