ConeMasher:Koni's, K&N, cat back, and a bigger front sway bar would be a great start, but 710's or A6's will transform the car. I and my different co-drivers are the only ones that I am aware of that have run the base model at national events. So far the car has been very course dependent. Great for sweeper and more wide open courses, but not so good on slalom or transition heavy courses. It is a good ProSolo car as it has a bit more hp than the MINI. I ran about an 1/8" inch toe out up front with zero rear toe to help with rotation, as well as maxing out the front negative camber. I cannot say how the car responds to sway bar/shocks as I have been on stock bar and struts the last few years. I have not won a national event, but have finished 2nd a couple of times. This season I actually ran the 215/40 16 Kumho 710 for better gearing. I was on these for the DC ProSolo where I finished second to GJ Dixon.
Definately run the 215/40/16 v710, 215/40/17 v710, or 225/40/17 A6, while you may feel you're not ready for r-comps the sizes I've recommended will force you to modulate throttle and braking more precisely because they will be very unforgiving with sloppy inputs. The problem with a 225/50/16, 245/45/16, or 245/40/17 is their overall diameter, yes they give you more tire to work with but the rsx (both base and type s) can barely get out of their own way on an autox course. In stock form the rsx also has a high cg so with a smaller diameter tire you can lower the gc while keeping the car's roll center's intact especially with the 215/40/16 which basically drops the car one inch compared to 225/50/16(22.6" OD vs 24.7" OD). Another plus is the tire weight savings, you will save 5 lbs per tire and to me saving 5 lbs of unsprung weight per corner is helpful. Now for the cons, like I said earlier you will be forced to modulate throttle and braking better, because while you've gained a gearing advantage your ability to hook up off the corner will be reduced due to reduced slip angle available. So once you've mastered control of you right foot the sooner you can put the gearing advantage to good use.
I do have to say this though, I have a type s, I have never driven on 215/40/16's but have used 225/50/16 v710's and felt the car lacked accelleration, it hooked up good off the corner but that was it, if there was a chance to let the rpms rise on course the car felt like it was in slow mo. Like Scott said the tire is course dependant and will shine on the wide open courses but I think with some good car control it can shine on the tighter courses too. I will be giving the 215/40/16 v710's a try next weekend at the BMR event and will come back and commentate on whether my thoughts actually manifest results.
My input will be this, get tires first and forget about everything else for now, try the 215/40/16 v710 and drive the crap out of them, learn what your car is doing but be conscious of your driving (throttle and brake modulation), improve your driving, then focus on where you're still having trouble and use dampers and sways to find a good balance in the car.
BTW since I've been autoxn (which really isn't that long), I've always felt the base RSX is one of the few cars that can present a challenge to the mini's and there just needs to be a few more people who feel like trying to prove it, so keep at it. Oh and the 215/40/16 v710's are ~$100 cheaper per set versus a set of 225/50/16's.
NYR STS #24 2002 Acura RSX type S
2007 NYR STS Champion