Some of the things you want to add to your car will make it heavier and slower, not faster.
The 17" rims are a perfect example. They are for show, not for go. They add unsprung weight (look it up), which is never good, and the extra weight increases braking distances. Also not good. Then there’s the price of the tires.
If I read your post correctly, your Integra has an automatic transmission. Is that correct?
If that’s the case, don’t spend any money modifying this car. An automatic Integra will never be a racer. You’d be better off trading your ls for a Type R Integra. That would be a better starting point for what you have in mind.
I think shadowfax has it nailed down. You’ll spend HUGE amounts of money before you have anything to show for it. Are you prepared to do that?
My guess is you’ll drive your automatic Integra around on its 17" wheels and pretend you have a race car.
Good luck.