Welcome to the site, Tim!
If you are thinking about eventually racing 944-Spec the 1983-1988 NA 2.5 liter 8 valve cars are the ones eligible.
The early cars (83-85) seem to be a little more desirable for track cars- they are a little lighter than the later (85.5-88) cars and the suspensions are a little easier to work on. They are typically less expensive to buy than the later car.
88's, though, have a little more stock HP, about 10, and come with a shorter 5th gear which is desirable at nearly all the tracks we race here in the Southeast.
Most racers end up with an early model car with an 88 engine.
Starting out in DE, though, I wouldn't worry too much about the year, just find one that is mechanically sound, has a decent body and is inexpensive. I've noticed a few good candidates on craigslist in Atlanta lately, there is also a 944-Spec racer in NC selling his old 944 DE car.
In addition to new brake fluid and pads and making sure the timing belt is recent, the only specific item I would replace before tracking would be the rod bearings.
These can be a weak point on the engines when they are tracked but are fairly easy to do yourself with a little experience- I'd be glad to help you with it. Also- some racers put a baffle in the pan to increase the life of the bearings.
As far as the other 944 models go, I don't have any first hand experience with the 944S or S2. The engines have a reputation as being a little more fragile than the standard cars and require more expensive/harder to find engine parts.
I do have have experience with the 944 Turbo on track- great power but it was very unreliable in my hands. I switched to an NA car and never regretted it.
What area of Georgia are you in?
EDIT: Grenadier's post reminded me that 87 & 88 924S cars are also eligible for 944-Spec. They are supposed to be a little lighter than 944's with better aero and the 88 version has the higher HP engine with the short fifth.
