Yes a motor can be swapped in or you can turbocharge the GE motor. Between the two you'll have to research to find out which one you'd rather do.
The GTE swap you will need the turbo ECU and harness. The motor will bolt up to the W58. The V160 six speed will also fit into the car but the driveshaft will need to be altered. I believe the twin turbos automatic driveshaft will be needed to mate to the V160/V161 to the differential on the Supra (no turbo). The differential isn't really the weak point, the tranny might be more of a concern. The W58 has been known to pop but it should hold the additional power fine. Some have had problems running low boost while other have achived over 400whp successfully with that tranny. Either way the six speed is superior but that tranny isn't cheap.
If you get a JDM motor it's a different story. You will need to either lengthen the wiring harness or buy a US specs harness and ecu. You will also need some additional sensors, a MAF, and the US spec injectors w fuel rail. JDM motors are cheaper to front, but you will need the extra parts to get it running. Plus, like the method below, you'll probably also need the intercooler and associated piping. Go straight to front mount $$, or but a used side mount off a TT owner.
Turbocharging is a nice option that can be done relatively cheap. There are varying results with this though. Many people (not all) seem to have problems eventually. If you really know what you're doing, then you should be able to have a successfully turbocharged 2jzge. If you don't have the shop space, tools, and technical background, you may run into problems. If you go this route, you will need the components. They do make "kits". Boostlogic makes a nice kit but it's also about five grand. You can buy a nice log style manifold from Dave Henry. He's one of the most knowledgeable and sucessfull tuners of the 2jzge. He makes a log style manifold as well as a few other parts. His parts are cheaper but have been proven to put out over 650hp.
www.boostlogic.com www.naperformance.com These aren't really fully complete either. They leave a few options out so that the buyer can choose their own parts...things like compressor bypass valves and whatnot. The nice thing is that these guys are willing to work with you. For example, if you want to drop the front mount IC and go with a a cheaper side mount, they'll do that...you'll be in charge of finding and fitting new IC piping though.
Piecing together a kit from scratch will be extemely time consuming. This is probably the cheapest method, but you'll have to know what parts you need and have the patience to find them. There will be plenty of parts you need for that project too. You need to be able to tap and drill the oil pans to run the return hose from the turbo. The cheapest route is to use a stock side mount intercooler from a Supra Turbo. Thicker headgasket, wastegate, injectors, afc, etc etc... Plus with two cats and a couple of mufflers, an exhaust upgrade wouldn't hurt. I could make quite a list of parts. Unless you go with the kit, you'll need custom fabricated intercooler piping.
Saving your cash and starting with a Supra Turbo is a better way to do this in most cases. If you want to drop in a motor or turbocharge the car, do allot of research. Especially if you turbocharge the motor. Unlike a few years ago, there's actually a good number of people that have done this now so read as much as you can. Find out what's worked and what hasn't.
If you plan on having someone do the installs, Id say forget it. Dropping a motor in might be more reliable than turbocharging the 2jzge. You can get more bang for your buck by turbocharging the 2jzge but it's not for the timid. Don't forget, if you plan on upping the boost, a thicker headgasket will be a requirement along with an upgraded fuel system. Basically with both methods though, you're your own tech support. Each was has it's strengths and weaknesses.