Unfortunately, I disagree on a couple of things here.
1) If you haven't really raced, got involved in motorsports, going out and buying a dedicated track car is a bad idea. You might not know if its the thing for you and you end up with nothing but a trailer queen.
2) Using your street car to start off, is a good idea, but you have to do it the right way - You do not spend time building up the car to a point where you feel its ready to be tracked, rather, you track the car as is and then find out what you need to do to build up to that next level (and then come to a point where you decide if the street car is not practical and you need a track car)
For someone starting out, I'd say, track your street car as is, join Supersprints in the stock class, get some track time.
You may decide that you could benefit from better brakes, shocks but don't want to go the whole hog as racing's not going to be your full on hobby, so you modify those parts and you can enjoy them on the street as well.
Then your times improve, you decide you need more power - ask yourself, are you going to dedicate yourself to the sport and race in some class (research the class, then you can either convert your car or buy a track car - whichever turns you on) and then work your direction from there.
For me, well, I would like a dedicated track car, but I can't afford alot the trailers etc etc, and also, I do like to take fun drives in my car as well - So I have a compromise, a street car thats track ready. Yes, I have a 2nd set of rims, but thats about it...