350's or 5.7L's (5.7L Chevy not Hemi) have been done for ages. Generally speaking the designation 350 died off back when GM went to EFI. These swaps aren't anything new. Out of all of the engine swaps the 5.7L is probably one of the easiest because it's the most common.
You will need a new radiator, engine mounts, engine harness, PCM, tachometer, transmission, exhaust, catalytic converter(s), and probably a new rear axle. I forget if you'll need to run a new fuel pump since it's been a while since I have looked into it. The easiest swap would be to use whatever transmissions that's connected to the engine. This will insure your ECM is correct for the engine and transmission type. Even though there is an adapter for the AX-5 you don't want to use it. Even AA recommends not using it.
For any engine swap it's best not to use adapters if you want to save money. By mixing and matching you'll end up having to use adapters for the engine to transmissions and the transmission to the transfer case. That's probably going to cost $1000 right there. So plan ahead. AA sells a weld-in as well as a bolt-on engine mount. Most 5.7L's are going to be automatics which isn't a bad thing. Depending on the year and what it came out of it will probably be a 700R4 (pre-'93) or a 4L60E 4-speed with OD.
The engine I would be using would be a OBDI which is up to 1996. The engine designation is the LO5 which was used from 1987-1996 and found on 1/2 T C/K10's These were pre-Vortec engines. The TPI will be easier to install then a MPFI system. For a Jeep it's best to stick with a truck engine then a car engine as truck engines are usually tuned for more torque down low.
You can get a new harness that will plug right in from Painless Wiring.
Oh I would also stay away from any engine that has a 'immobilizer'. They can be a PITA to get working right since you have to program the key to the ECM. If you don't do this the engine will not start. There are places that do this but that's an additional expense.
Well, that's it in short. I've left out a lot of little things.