Just get some decent shocks/springs (I went with tokico illuminas/h&r sport), some fresh wheels, and a yonaka exhaust. Make sure you have the wheels set up properly and don't buy anything heavier than your stockies. Enkei RPF1's are a nice example of a decent affordable wheel.
It's really easy to make an Integra look nice, but it's also easy to make it look like a bowl of rice. Making an LS auto loud will just be embarrassing. You're not going to beat anyone in a race and you'll give the Integra a bad name. LS's aren't meant to go fast, but they can look really nice and bitches still dig em.