My experience is 99% with autocross, but many of the same principles apply to track. You can build a pretty capable Fox Body that retains the stock K-member, A-arms, and uses a stock-style (non coil-over) spring setup. Ideally, you want to get the car neutral, add adjustability, and address old bushings.
A track car can be lower and stiffer than an autocross car, but setting your car up to be too low and too stiff will lead to understeer and oversteer (making the car handle worse). The Sportlines are pretty low. If you watch my videos, you'll see that my cars sit pretty high. With a stock-style spring setup, these cars handle better when they aren't lowered very much. It doesn't look cool, but it works.
Adding adjustable shocks & struts is the best mod you can make to improve the handling of your car. They allow you to add/reduce understeer/oversteer to compensate for, or capitalize on, other mods. These cars came from the factory with understeer. Your goal is to get the car neutral, and to move the limit of traction further out. DA struts offer more adjustability, but it might be better to do SA Koni Yellows in the front and rear. The kit costs about $700. Being able to adjust the car at both ends is really important. If you can do DA at both ends, that would work too.
I would also suggest getting a larger rear sway bar. A 25mm
Eibach rear bar will add oversteer, helping to balance out the factory-installed understeer. With the CC plates, the adjustable shocks & struts, and the larger rear sway bar, you will end up with a car that handles better than stock. It will also be a solid foundation for the more personal mods that you'll choose later, based on your driving style.
Check every rubber bushing on your car, and consider bushings that will improve performance. Global West Del-A-Lum A-arm bushings are offset to add caster. That will help with composure and corner entry .
J&M spherical upper differential housing bushings will help with the "nervous" feeling in the rear end (along with a good set of UCAs with 3-piece poly bushings).
Knowing what each mod does in terms of understeer and oversteer is really important. Here's a video that will help:
View: https://www.youtube.com/watch?v=9HiS-t4_O_w&t
From a safety standpoint, the OEM disc/drum setup isn't up to the task of track days. Repetitive high-speed stops will expose the limitations of your brakes pretty quickly. The safest thing to do would be to invest in 4-wheel disc brakes when you can. You want brakes that will teach you to avoid the penalty of using them too much, but will also be there for you when you need them the most.
If you have any more questions, please ask here or in the comments on YouTube.