For performance modifications for the MKIII Toyota Supra, the best company is HKS.  They offer 8 steps to get 453hp@15psi.  Even if you don't use all of their products, they offer a nice general outline course of upgrades that make the Supra a heck of a lot faster.

Stage	Modification	Picture	Horsepower
1	Cat-Back Exhaust  (recommended  with 3" downpipe)  HKS, Apex-I, Pacesetter,  Greddy, Blitz		251hp@8psi
2	High-Flow Air Filter K&N is the only  way to go		259hp@8.5psi
3	HKS EVC IV HKS		285 @ 11psi
4	Intercooler   HKS		298hp@11.5psi
5	PFC-FCON HKS		330 @ 11.5psi
6	Vein Pressure Converter HKS		345 @ 13.5 psi
7	Sport Turbo Upgrade, 550cc injectors HKS		438 @ 15psi
8	Cam Shaft, Cam Gears AEM, HKS		453 @ 15psi

-- The Catalytic Converter is very restrictive and most states don't care about emissions any more (make sure to check about emission requirements in your state).  Get a test pipe made and replace the cat with it. Either get a foot of pipe with two flanges on either end or shove a 2.5" pipe into your hollowed out cat.

-- Cold Air Mod:  Get some kind of rubber or metal hose 3" in diameter and run it from the grill to the filter. Remove the engine cover on the passenger side under the headlight for better access.   Isolate the heat of the engine bay from the filter/intake for best performance with sheet metal or a box of some sort.

-- Intake Piping: Get rid of the stock intake resonator and increase air flow a little.  Buy a section of a 3" pipe from a muffler shop and trim the first rubber intake hose so that the ribbed section is gone.  Stretch the rubber hose and then put the pipe in with the help of some WD40.  There are company's that make pre-made intake pipes, but why spend over $100 when you can get the same thing for $15?

-- Headers:  Pacesetter ($219) makes these, but from what I have heard is that they're a real hastle to put in. They have to be altered to fit and should be coated with ceramic coating (expensive) to keep the engine temperature down (so performance won't be hindered).

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Links:

Bishop's Supra Page:  Contains a helpful Upgrade path for MKIII N/A Supra
Modacar: List of Exhausts offered for Toyota's including MKIII and MKIV Supras with pics
SOGI Members' Pages: See what other Supra owners have done with their cars
MKIV.com: Site devoted to MKIV Supras with lot of info on upgrades with pics