I would hire someone who is fairly knowledgeable with autos to check it out with you, or for you, if you are not all that familiar with them. A service tech would be a good idea but not absolutely necessary. There are many of us out here that know autos well enough to do a thorough inspection. Since you are buying used, you might be able to afford some features that if you were buying new, you wouldn't be able to afford. Some features are worth having and some aren't. It would be difficult to go through all of those with you on a forum but if you have any feature specific questions we could give you some insight on those.
Looking for issues that a press might have is like inspecting a used car. The most important thing to look for would be if it holds registration. That would require you setting up a multi-colored job and looking at each pallet to see if there are any inconsistencies. As the press indexes and the table moves up and down, look for how smooth the press operates. Same goes for each print head. See if you can find most of the grease fittings and if you can tell if they have seen a grease gun recently. You can tell by the looks of one if it does or doesn't get greased regularly.
There are only a few manufacturers that I would stay away from as far as used machines go and I wouldn't consider anything older than mid 90's on any press except for the American Centurian. There may be other exceptions to that as well, but that's a good place to start.
Look for a servo driven indexer and AC print heads as far as major features go. Air indexers and air operated print heads are fine, but if you have a choice in the matter, choose electric. A lot of the other features will come down to personal preference. I chose a press with every feature you could get without really knowing how it would affect day to day printing. Turns out I use every feature on our press. I know some printers would have no need for some of the things on our press, but most features, when used properly will save time.
Not to put any pressure on you

, just reminding you as to how important this process is. The press you choose could make or break you, so be diligent and educate yourself to the fullest. Good luck and keep us posted, we like hearing how it all goes.