By this point Kez you must have noticed that there are some very clear pros and cons to both sides of the equation.
I've done both and for me and what I want from track days and the car, a dedicated car was a better choice.
When I had the GTST and then the GT-R (both streeters) the compromise of needing the car for work (and I actually used my car for work not just getting to and from work) meant I had to make big compromises in setup, mods, legality, safety, noise etc. Don't get me wrong, I loved having them both as daily drivers but the cost of maintenance and the above compromises made me move on. I was also a bit of a knob and lost a stack of points on my license and paid a few bucks in fines, that's another topic though, my point is just that there was more temptation for me, you might be more mature than I was at that age, it wouldn't be hard
I opted for a pretty cheap track car and a reasonable daily. So the BA makes a great work car and tows the S13 with ease and the S13 can be driven as hard as I want (though I tend to be cautious "most" of the time - broken stuff costs $$) and I don't have to worry about getting it home or getting to work on Monday. I also don't have issues if parts are out of stock, take ages to ship or I need to save funds before I can fix something. It just sits there and gets started from time to time.
Further more, My particular track car has remained street reg'd, no way is it legal but I can get away with driving to and from workshops as required which avoids the issue Dane was mentioning.This is the case because I bought a stockish reg'd car and built it up myself, which is heaps more expensive I might add. You can do that too living in Vic where we don't need yearly RWC.
Buying a dedicated and built un-reg'd S13 or 14 is great value, but I bought my car to build and learn myself and I also love being able to drive it around the block or to a workshop as required - I just ditch the semis and big spoiler.
In the end, you have to work out what is best for your current situation and financial capabilities. Keeping your supra, doing some basic work and having some fun at the track is the cheapest way - big accidents and part failure aside - but it's also a compromise on performance the whole "drive it home/to work" issue. That said you will still learn a heap in a Supra at the track without big power. Even driving my BA around has taught me a few things because it's so big and heavy.
It's important to know what you can afford to spend before you can make a clear decision, it's also important to have some idea of what you want from your track adventures. Some guys are out just for the fun of it and some are out to be a bit more competitive, get times/drift better, and develope the car. Both are valid reasons to be at the track but each can be achevied in different ways.
Good luck