Ok, for 350hp you're going to need the following:
- An engine in good shape, including hoses, gaskets, etc.
- Intake - I suggest a Blitz or AEM air filter
- Exhaust from the turbo back. Personally I used a BIC DDP and had a local place fab me up a full 3" pipe from there back
- Something to increase your boost. I'd suggest a MAFT Pro with the boost control kit
- A better intercooler and hardpipes
- Bigger fuel injectors, an adjustable fuel pressure regulator, a walbro fuel pump, and something to convince your stock ECU that everything is still ok. The MAFT Pro will do this as well. There are other routes to this, I like the MAFT for various reasons.
- At this point, you should be able to tune for over 300hp. If you want to get closer to 400, you're going to need an upgraded turbo as well. A 57trim CT upgrade would do fine.
If you go this route, you're going to need better brakes, *much* better tires, and a better clutch if your car is manual. If it's an auto, you'll likely need a new tranny. Living in California, you're probably going to need to work on the cooling system, too. A fan shroud and engine bay undercover is a damn fine start.
Furthermore, get your rear subframe checked for cracks. Anyone who drives hard on a stock subframe at 350+ hp is likely to crack it in several places.
PS: IMO, If your Supra is your daily driver, I'd never drop below $2k in your Supra fund until there is an emergency. There WILL BE emergencies.
PPS: A car at this level will kick the absolute snot out of pretty much 98% of the vehicles you meet unless you are at an actual racetrack. Then it'll only be faster than about 75% of them. It's also up in the dangerously fast category, meaning, it's not difficult to get out of your capability to drive and end up bleeding in a ditch, surrounded by a cage of twisted wreckage.