I imagine you can hit your goal much less expensively, but then you won't be ready for your next goal when you get bored with 350rwhp. There is an advantage to modest HP goals in reliability, tuning the power and torque curves to best driveability, fuel economy, and low turbo lag. Maybe you should give us a better idea of what the car will be used for. It's a beautiful body, but that's only lust, true love is about the relationship.
I would think the basics are unrestricted air flow, so naturally new intake/filter, lexus AFM, downpipe that replaces the turbo elbow, high flow CAT or test pipe, catback setup. This will make you not-street legal. If you were in MI there is no inspection, so you can get away with anything. In Ohio, I don't know. You need to get the whole airflow path clear before worrying about your head. You need to plan your exhaust manifold/turbo/downpipe together, since they need to mate up. you can hit your goals with stock turbo and manifold, and good downpipe back, which I have, but I wish I had a way to relieve back pressure above a certain level with a pressure sensitive exhaust valve that vented to an open pipe leading under the car, like the downpipes for the external wastegate setups. I think that would let the car really scream and boost when you stomp on it hard, but still allow normal flow through the cat and muffler in normal driving. Just an example of how little decisions now become unexpected limitations later when you are not realistic about your own power lust. Hardpipes and a new intercooler are easy to add later and not necessary for your goals.
Once you have the intake and exhaust paths clear you will need to do the head gasket. That is the absolute before you can get to substantial power. That's when it will be tempting to take out the motor and rebuild everything. You don't have to do this to meet your power goals. You get the most power per dollar from boosting on the stock turbo. A simple manual boost controller via adjustable bleeder valve is a cheap way to experiment, and you can add fancy electronics later. Combine boost with Lexus AFM and 550 injectors is a well traveled path that works well. You can boost from stock (7-9 by various sources, I've never driven an unboosted supra, so I don't know), to about 12-14 before you need to deal with fuel cut, then start talking about piggyback electronics and new fuel pump and regulator to get a bit higher before you are just blowing hot air from your compressor without further air density gains.
All this will get you well past your goal, without a new turbo, touching the bottom end at all, or even reworking the head (but then where's the fun in that?). And you can do all this for about the same as properly rebuilding the engine.
If you just have to tear that engine apart and rebuild it, do it right the first time, if you have the experience and skill, or have the bottom end done in a shop, or exchange it for a rebuilt one. The head is easy to work on later, but pulling the engine is a lot more grunt work and more risk of scratching or denting that lovely body. In retrospect, I really wish I had done upgraded rods, pistons, rings, rather than just regrinding the crank, cleaning the pistons, and doing new bearings. it would have cost another $1500-2000 for new stuff, but I've seen people selling unused rods and pistons when they abandoned their projects. In fact, i'm going to tear the whole thing apart again to do it right. If your bottom end is good, why not leave it alone and do the easy stuff until something wears out or breaks? In the mean time you can watch for good deals on the quality parts for the full rebuild. Or just find a built engine and sell yours ($ smart, but totally lame, IMO).
