get a vtec box. it fits in your glove compartment fairly well. it'll also give you an instantaneous 200 whp boost!!!
just playing dude. i/h/e is a good start. when it comes to enhancing the performance of a car, "cheap" is never a word associated with power. Perhaps invest in a cold air intake system-AEM is nice. with the ls motor you have, its real torqy so get a nice header. a lot of people would suggest dc cause its affordable, but I would suggest a tri-y (search for hytech/rage header) header. For exhaust, I would suggest an HKS. Its very subtle and not annoyingly loud and very rare.
I'm not entirely sure what you mean by making your car "handle like its on rails" but I'm a fan of full ground control coilovers. kyb agx 4 way adjustables are nice as well. I use it on my 98 integra. rides like stock.
if you plan on wanting more power and have more $$, if you choose the NA route, it'll be very very spendy. most will suggest forced induction (turbo/supercharger)-but that's also costly depending on the amount of power you want.
for now though, i/h/e is good enough since you say you're still new to this whole integra thing. its good to slowly progress. that's my take on it. gl!
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