Stock internals can handle that much power but I don't know how long they would hold up. How many miles are on the motor. Sounds like you'll have a fair amount of funds to put into the car. I'd do it while you still don't have too many expenses
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But again...how many 350 hp cars have you driven? 350 whp is also more like 400+ hp at the crank. All that on a mid engine, rwd car that has no driver aid systems like the new cars...might be more than you're ready for. I don't know how much driving experience you have but I've seen plenty of people overpower their cars before they're ready. I'd keep the engine close to stock...maybe a few bolt-ons and spend some money on track time and skid pads.
Ben on the boards is running around 350 whp with the twosrus.com street brawler kit. I know he did a full rebuild and spent around $10k...