Ok, you're getting some decent advice here, but let me put it all together and add a bit more.
First up, that Camry isn't even vaguely close to a plain Jane people mover. It's a 270hp car that weighs in at 200lbs less than your Supra. That's nearly 40 extra ponies and a fair bit of weight.
You would need ~280 hp to match that without losing weight on your car. This is easy to accomplish, a drop in air filter and a full 3 inch exhaust (downpipe, high flow cat / test pipe, catback) will get you there. Actually, a DDP (Divorced Down Pipe) will likely put you over by a fair bit. Adding a manual boost controller - and for the power levels you are talking about, it's the best solution by far - will put you up around the 320 at the crank mark.
An exhaust that looks completely stock is not hard to come by.
I would avoid the HKS downpipe, it's rather more restrictive than anything else out there. I'd also avoid an EBC, they are a pain to connect and get properly set up, an MBC is a much better choice. For an exhaust, I'm actually reasonably impressed with the look of the dual output unit that ETS has just introduced. For downpipes, you cannot beat BIC's DDP. For a MBC, you cannot beat the unit that Dr.Jonez sells.
Living in Arizona, you need a filter that works for dust - the AEM dryflow is a good choice. The oil based filters, especially the K&N, should be avoided at all costs.
You will not need a new turbo, injectors, intercooler, hardpipes, or anything beyond these three parts. Your transmission should hold up fine. I can't say the same about your tires, though...
I'd be surprised if it takes more than $1000 to put your Supra back in the top spot.
PS: Keep some coin on the side just in case. Parts that could handle the strain just fine at 230hp are going to decide to retire early at 320hp. Particularly engine mounts - get them checked before you start these mods, and check them often... I snapped my first set at about that level.