From what I've read across many forums, auto-x discussions, and track threads : Usually on the civics somewhere between 1.5" and 2" is the largest improvement in handling area. Beyond that you start compromising roll center and stuff like that. Unless you are going to get extended ball joints and correct your suspension angles and roll center you will have "worse" handling characteristics.
Again a lot depends on the suspension setup you are running, wheels, tires, camber, and all that sort of stuff. The HPD NASA rule book says the cars must have a minimum ride height of 4" at the rocker panel. But again, those are race cars with "fully" adjustable suspension setups. They are beyond modified with a set of coil overs.
Lots of people are very happy with either the eibach or the H&R springs.
The strut will make a huge difference in performance as well. If you wanted to go crazy and get double adjustable race struts and custom spring rates I bet you could make the car handle fantastically at any ride height. So it really just depends on budget and what you want out of the car.
I would advise against slamming the car and scraping everywhere but hey, if you want to do it, then do it. Don't get what someone else tells you to, do what you want and you'll be happy in the end. I've played that game and wished I had done what I wanted in the first place. Oh well.
That said,
I would recommend you a drop in the 1.5" range. A quick set of springs when you're on a budget can do that in a pinch until you either upgrade the struts or get a different setup. Coil over sets are great since they include a strut. They start as cheap at $600, for a set I would recommend, to around $1000 where you have a lot more choices. The coils I have seen below the $600 Megan EZ Streets have been generally garbage. I would stay away from any coil over setup that costs less than springs alone.
(EDIT: I'm at nearly a 2" drop and when I was living in upstate NY, there were definitely a few days I was plowing snow. No problem if you have good snow tires though.)
