For 50 grand, there is absolutely no reason not to get the right tool for the right job and get two separate cars.
Tracking a street car is a compromise that makes less sense the longer you do it. Most street cars can't handle the stress of sustained track use and cars that are made good for the track are usually a pain to live with on the street.
If you live in a place and have the lifestyle and disposition to drive around with 5 pt. harness, metal bushings, 1200 lb. springs, no A/C or interior and a set of slicks that cost twice as much as your TV, then more power to you. But most of us would prefer to get on with our lives in, you know, a real car.
Plus, you have to ask yourself if you're ready to ball up your shiny $50k car if something goes wrong. Track days are generally very safe, but if bad stuff happens to you on the track, your regular insurance company isn't going to a bit of help. So unless you are ready to pay an extra several hundred bucks on track insurance (on top of fees, gas, food and lodging), a dedicated, inexpensive track car is the way to go.
My picks? A decent C5 Vette for around ~15k. Tires, brakes, suspension, seat(s) and you are good to go. Later you can pull the interior, add some power, add a half or full cage and make any changes that are needed. Figure roughly 8-10 grand to do all that. That is a lot of fast for not that much money and should be enough hardware to keep most people entertained from novice to advanced run groups.
With the leftover money, I'd get a 2-3 year old E90 BMW 328i and leave it bone stock to go to work, shuttle kids, shop for groceries and take the wifey to dinner in.
M