First thing to do is get a GCR, and determine where any of these cars are classified. The 93 Acura is classified in ITA, if it's not the "GSR" version. I've only seen a few of the 2nd gen Integra's competitive. Not sure about the 3rd gen.
The 86 Prelude is classified in ITB. Eclips is classified in ITA, but I haven't ever seen one on the track.
The Acura and Honda have many go-fast parts available, so if you already have the Prelude, I'd start from there.
Things to start out: Is the Prelude running? If so, don't touch the engine. Get a header, baffled oil pan, and an oil cooler. Remove all of the interior, head liner, sound deading junk, leave the dashboard, heater core, and blower. You might need those depending upon where in the country your at.
How are you planning on getting this thig to the track? Drive it? Tow dolly it? Trailer?
You'll need at least the following: 6 point cage, 8 point would be better. Bolt in is the cheapest, but only meets the minimum safety requirements. Racing seat, window net, 5 point harness, fire bottle, DOT racing tires on your stock rims, Hawk or some kind of racing pad on your stock brakes. Don't also forget your safety gear. 3 layer suit, nomex underwear and socks, gloves, helmet, racing shoes/boots, beleclava.
If that doesn't eat up all of your starting budget, then I'd go with coil-overs with camber plates, steel braided lines, LSD for your diff, aftermarket (lighter) wheels.
Hope this helps.
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Tim Linerud
San Francisco Region SCCA
#95 GP Wabbit (Bent)
http://linerud.myvnc.com/racing/index.html