For $5.5k you might want to set more modest goals, it will cost more than that to do what you're proposing.
The SR20 isn't a bad choice for a car like this, but the engine bay is pretty small so you might want to get your tape measure out. If it was me I'd be looking at the 4A-GZE, it's very compact and will fit easily.
The Hilux diff is overkill at this power level, but if you do go down that path you can adapt MA70 Supra brakes relatively easily. GiantTomato posted a guide on how to do this, if you search around you should be able to find it. It was a while ago so it might be on the old forums.
I wouldn't be too concerned about the rear brakes though, what you really need to do is upgrade the fronts. The tiny discs on a TA22 are barely adequate for the stock 2T, let alone a modern turbocharged engine.
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