If you're an experienced driver and could expect to be pushing the car somewhat, I'd upgrade brakes and safety gear in that order. The car will run hot when run hard, but shouldn't actually overheat (the motor actually makes the best power just short of temp red line). The upgrades I'd make in order as as follows:
1. Motuls (or equiv) Brake Fluid and front brake air deflectors
2. Stainless steel brake lines
3. Teamtech safety harness, driver and passenger
This would cost around $1000 all in (
www.partsrack carries all of this stuff), and will add a margin to your braking performance. For 3 or so track days a year just the above gives you a solid car. Going forward, I'd do the following:
4. Stoptech Slotted rotors
5. Eibach springs, .75" lowering
6. A good track alignment with extra front camber
7. Upgraded cooling fan from a 99+ Viper
8. PartsRack Stage 1 & 2 Oil kit (deep pan, baffles, windage tray)
9. Autoform Roll bar
10. Magnecore spark plug wires & plug heat boots
Beyond this, you get into the expensive upgrades, have a trusted Viper Tech advise you on the best place for your money. Plus, a few subtle things:
A. Viper motors are weak in the #3 crank bearing, so pay special attention to big left-hand sweeping turns. That clicking sound from the motor? That's your engine starving for oil. Consider installing a bright low oil pressure light and back off if you start to hear loud ticks from the motor in corners.
B. Your car makes too much power as it is. Spend your money elsewhere after you've done the cheap stuff. I personally know a guy who dislocated his shoulder because he rubbed a wall in his 800HP tuned car with stock seat belts.
C. Get some track wheels if you're going to do more than a few track days per year. If you use 17" 5-spokes, don't use wheels from a 96 because they're weak. An especially good buy are Purner anodized wheels - they take a hell of a beating and don't show brake dust.
D. The stock brake pads are Brembos, and are actually pretty good, but expensive. The best bang for the buck are EBC Yellows - I can run them for 2 track days and they cost something like $100 for fronts. I run EBC Greens on the rear.