After buying a MK3 that was "clean" and near mint condition... to find out it was about to have a lot of major issues, I have a few suggestions...
1. there are 2 doors in the hatch area. when looking into the hatch, the one on the left is the first one I open. Put your arm in there and feel the edges of the wheel well and reach as far down as you can (you can feel almost the whole quarter panel from that door).
Do it carefully because if there's bodywork.. it could be messy with sharp edges.
If you find a lot of water and dirt, then you will probably find rust along the seams and the wheel well needs to be pressed against to find out if it's rotted. Undercoating usually allows for this as tiny rocks perforate it and allow dust and water to be held against the metal to eat its way through.
The door on the right is access to the antennae area and quarter panel. This one is harder to check. With a little maneouvering you can get to feel that quarter/wheel well as well.
The tail light seals will allow water into there as well as the spare trunk well. Take the spare tire out and check for rust. Its quite common to occur there.
Then climb under the car and look on the inside of the rear bumper and check the brackets (mine were rotted enough they almost didn't exist). Look at the rear suspension and the diff at that time. Usually a bit rusty, but very heavy rust could indicate issues that you want to look at closer in that area.
2. Bring a CO2 tester with you. 50-85.00 to get one and will tell you the one worry everyone has ... is the head gasket solid? Run the car a couple minutes.. then use it as directed and you will know a lot. Any slight change from blue to green is "head gasket replacement time" generally speaking.
3. Rock the wheels up front to check for the ball joints going. (lowers are common to go out and not that much to replace.. 85.00 and about an hour)
Look closely at the louvres behind the driver and passenger windows (the black plastic pieces). Look for any metal bends or rust there and along the base along the triangle windows of the hatch area. Common place for rust. Also along the a pillars to the left and right of the windshield.
That is basically what I do before driving any MK3 that is for sale.
Also, consider that a 6000-9000.00 Supra with bills showing all the work/parts is normally worth a lot more than they are asking. If the body is tight, paint very good and interior clean, the additions (especially if its 1j or 2j'd already) will cost you more to do than what your paying for the car. The 1j/2j swaps though can be done at home in the garage, but I have seen a lot of hack-jobs that sent me running. It has to be done properly or you probably wont be happy.
You already know you want to go 2j.. so buy one that is done. TAKE YOUR TIME hunting! The deals that pop up from time to time are incredible.. just because some people outgrow these cars. You can take advantage of that. Like the Cherry Widebody I missed out on... I had a MK3, or I would have gave him asking price without blinking an eye.
The reality is.. after putting 45,000 into a MK3.. its still only worth somewhere between 4000 and 19,000 depending on what buyer a person can find and timing. You wont get your money out of it.. so why not be "that guy" that gets the bonus.
I probably would consider cars for sale in these forums because you get to read their build history as well. Patience is key to saving money and headaches.
Those are my thoughts.. hope they are of some help.