CJ5's are notoriously wobbly, but should not do what this one is doing. The problem with buying a modified or in this case "restored" jeep is that the quality of parts as well as the expertise of the installer are unknown values. If either is questionable, you probably will end up doing it all over again.
Generally, CJ7s are preferred over CJ5s. If you want to get rid of carbs and go with fuel injection yet keep the ease of repair in the pre-air bag vehicles, go with a YJ. If you want even more reliability and good highway ride, move to the TJ. No rust should be noted on any of them. If they are rusty, pass. There shouldn't be rust on a Texas jeep. You should look for a completely unmodified unit. Modifications are shunned for the same reasons that restorations are shunned.
No matter your decision go to the following to start your search here:
It is easier by far to learn in advance than to repair.
You are looking to buy a jeep for exactly the same reasons I bought one: To work around the farm and to drive into town two or three times a week. I have no modifications because I don't need any. The land around me is very much like the land around Dallas, so I don't need any expensive rock climbing lifts or 35" tires. To do any rock climbing I would have to import the rocks. I have reached the age where I don't need to look cool to the kids anymore, so having to climb a ladder to reach the steering wheel is not a deal either. I have pulled out the factory carpet, cleaned the floor pan down to the (unrusted) paint, put in a new timing chain (154,000 miles), got new seats, and polished it as best as the chipped paint will allow. Soon I will put new springs in it, as it needs them. It is completely stock and in 4-WD low will go anywhere I want to go and some places I don't. Cruise speed is about 60 MPH with the 2.5 liter four cylinder.
But ya' know. In the summer when the top is off the wife and I still get waves and people come over to talk to us. It just makes people happy.