A torch is cheaper and probably more flexible in the long run but takes more skill to opperate. I'm a hack so I bought a plasma.
Spend the extra money and buy quality tools. Miller Makes exellent welders and plasma cutters.
Welding the diff means welding the spider gears together so both tires turn at the same speed all the time.
The biggest decision to make up front is tire size and axles. If you want to run 35"-37" on a light weight rig stick with the toyota axles. If you think you will end up running 40"+ and a powerful motor build dana 60s from the start. 60s cost about the same to upgrade as toyota axles but buying the axle can be expensive.
Fix the over heating problem on your 22r. If you fix this it will sputter and choke along forever but overheat it badly once and it could be ruined.
As for engines the 3rz (tacoma 4 cyl.) and 4.3 (chevy truck v6) are both popular swaps. They are both reliable and make good power. The 3rz will bolt to a w56 with a tacoma bellhousing. I am in the process of putting a lexus v8 in my truck. These motors are cheap but it would be a tight fit if you want to keep your factory sheet metal and it is also much cheaper to run an auto with them.
I have never had a truck with a carb but many on this board run them. If you can narrow down the problem someone can probably help you.