You should look around for 1jz/2jz forums, the swap's been done before, but I'll try to answer you for a bit.
Fabrication wise, you don't have to do anything if your supra is a 89+ model that uses the round style engine mounts. This is also assuming you'll use either the w58 trans, or the r154 trans with a 1jz bellhousing.
Parts wise, it can be a long list depending on how much you get with your engine. Assuming everything is on the engine, you'll need a new throttle cable (mine's from a corolla
), possible clutch line depending on what trans you originally had, electric fan kit(if you don't want to use the stock clutch fan), power steering lines (both return and pressure side), and a majorly overhauled wiring system for the ecu.
There are other odds and ends that i'm probably forgetting, but if you search around you'll be able to find interchangeable parts between the 1jz/2jz/7m engines as well as wiring suggestions and tips.
And from word of mouth, the 2jz stock internals can handle upwards of 700 rwhp, but don't quote me on that, as I don't work with that engine often. But there's enough documentation out there to prove it.
If you need stuff, you should try driftmotion.com .If you need swap parts for the 2jz, they'll have em, and upgrade/aftermarket stuff as well. Have fun.