Electrical
This is something that gets hours and hours of attention and discussion. At very best you have an electrical system that is 30 something years old and most have spent significant time in hostile and corrosive atmospheres. At the very worst one or more of the previous owners considered his stereo system to take priority over things as foolish as tail lights. The obvious conclusion is that the more pristine and original the wire is in the easier it is to keep everything running. As always be cautious of the seller who starts by telling about the killer system and/or the 8 day lighters that replaced the high beams.
Good indications of electrical challenges is the number of splices you see with duct tape insulation, before I get jumped on here there are a couple of these from the factory but these would hopefully be wrapped in convoluted tube. Wire nuts and "scotch locks" are a definite no-no. Look at the fuse block. fuses wrapped in tin foil and spent 22 shells are always a dead give away of possible problems. Soldered splices, when splices are necessary , are my first choice but not every body is talented with a soldering iron so if the lump under the heat shrink is a bit large it may be time to pull the pocket knife and take a closer look.
After market wire harnesses, are not magic or blessed from on high and when you are through you don't have the luxury of a factory diagram telling you what color what is and where it is supposed to start and end. If your buying a machine with a replacement harness you already know for a fact the PO has had his way with every wire in the entire system. Tell me that gives you a warm secure feeling.
Having taken all this into consideration, keep in mind that 80% of your problems will be electrical 10% will be vacuum leaks and the other 10% will be deciding what size tires to run and fun easy stuff like that. Of that 80%, half of those will be bad ground connections. Grounding failure is directly proportional to rust and corrosion. Keep this in mind as you are examining the body, it isn't just about looks.
There are enough threads on trouble shooting 12V DC electrical systems and proper use of a VOM that this is not the place to discuss it. As vehicle electrical systems go you are not going to find an easier system to understand or work on than the CJ. Do be prepared to spend some time with the electrical system and if you don't think you can ever get your head around a wiring diagram or be able to learn the difference between volts and ohms you may want to rethink this whole thing before you become the PO that the next guy blames for all the electrical problems.
Emissions
Way back in the 70s the United states government, going under the name of the environmental protection agency, called all the engineers from all the automobile manufacturers into a big meeting room. The head EPA guy then set down the new rules. "What we want is to be able to throw a large basket of meadow muffins up into the air at speeds not to exceed 55 MPH and when these meadow muffins once again fall to the ground they shall be transformed into, not less than, 10K gold." and you know what? they did it!!
We lost a lot of the horses that we had previously associated with those meadow muffins and things, in general, got a lot more complicated under the hood. We were on the way toward saving the planet for future generations of both humans and polar bears. A truly noble cause, I do believe.
Now lets flash forward 30 something years to those of us that are looking for our first CJ. We are looking at decent looking CJ that runs more or less and the current owner is so proud that he removed all that Damned smogg junk and threw it in the dumpster where it belonged.
Now, after a little history and a return to the present the big question is what is "the emissions system" and why is it important to me when I am looking for my first CJ.
the emissions system is the equipment that controls the production of pollutants into the environment. that is pretty broad and not worthy of Wikipedia but it's the best I got.
the first and most obvious is the evil empire dictates that some of us who live in liberal controlled western lands and most major metropolitan areas must maintain some level of participation in this program. some of us are not required to have a probe stuck up out exhaust but even these may be required to at least have the offending equipment installed , even if it does not work. This in mind, it may be a good thing to at least own an air injection pump and mounting bracket even if there has not been a belt on the pulley for a few years. Interesting point: you can still buy a pump, air injection manifold and check valves for the AIR system what you can't pick up at the local parts house is the pulley and the mount, the hoses are also something that will require a bit of creativity. So be forewarned!! know the law and what your responsibility to it is. You may find that the "pretty good deal" will never be allowed on the pavement again. I always thought that "all terrain vehicle" included asphalt.
Why do we hate Emissions systems? I think that it is because the available information on the system is minimal at best. If you have to put one of these systems together from point zero your going to have to do research to put the history detectives to shame.
What to look for: there are several very good and worthwhile parts of the system that are very worth saving. The TAC, thermostatic air cleaner. This air cleaner has a damper system in it that is controlled by a coolant temperature switch and powered by manifold vacuum. It draws warm air from the heated chamber mounted to the exhaust manifold until the coolant is at operating temperature and then it switches to cool air through the main intake and possibly a cool air duct routed to the front of the grill. Now considering that the Jeep engine is possibly one of the most cold nature d machines in existence, I figure this is a good thing to have.
The EGR valve, exhaust gas recirculation valve. Now how could putting exhaust gas into the intake manifold possibly be a good thing? come to find out that mixing a little carbon monoxide with the combustion process not only causes a drop in some flavor of bilge the internal combustion engine is so good at producing but is improves fuel efficiency and will make the engine idle smoother. Who would have guessed that!! the PCV valve. this little jewel allows the oil vapor and cylinder blow by to be sucked into the intake manifold to be efficiently burned rather than released into the air. with out a properly working PCV valve you engine performance will bring the meadow muffins back to mind.
There are several more things you will encounter in this part of the adventure like the electric choke, the charcoal canister and that most infamous of all the catalytic converter. Interesting point for all but those in the far western lands, the 1977 CJ was the last year to come from the factory with NO catalytic converter!! You may want to keep that in mind. Every time I envision a catalytic converter I think of driving across a field of tall dry grass with a cherry red piece of steel hanging under the frame.
Now to close this, the bottom line is, obviously, look for as close to stock as possible, just because you do not yet understand it does not make it a bad thing that must be removed and discarded, the society of automotive engineers did not do anything terrible and stupid although a group of politicians more than likely did. The average automotive engineer is for the most part is a pretty sharp guy or gal and they gave us the best tech available at the time, there is better tech today and we can take advantage of some of it but there is a lot of the old stuff that is still valid and we would do well to learn of it and take advantage of it, after all that's one of the reason we have a CJ.
For all you nubes and pre nubes I bid you welcome and wish you luck on this, the road to enlightenment