Welcome! How did you come to that number, exactly? 350 whp equates to around 440 brake horsepower on our cars, roughly double what you've got now. See where this going?
You will need a much larger turbo than the TD04 you've got, plus all supporting modifications such as fuel pump, injectors, larger intercooler, downpipe, and maybe an E85 setup. If you want that engine to last, I would look at a full rebuild with stronger internals. Now that you have a 400 horsepower car, you're still using the stock suspension and even worse, the stock brakes. The stock brakes are barely adequate for stock power levels, so you'll definitely want to upgrade those (that should be a non-negociable line item in your budget, seriously).
Have you driven a 400 horsepower WRX? If your car is stock now, you'll be quite pleasantly surprised with a Stage II setup. Read the engine forums stickies to learn more about good starting modifications.