We have a Lithrone 28 which runs very well for us.
Depending on what kind of work you are going to be doing, investing in an Aqueous coater might be good, especially for coated papers.
I'm not going to give you the whole rundown on how expensive and a learning curve offset printing is, I'm sure you have already researched that. So a checklist I would give you is:
(1) The impression and transfer cylinders should be in good condition. This can be very important if you are not willing to spend 10's of thousands of dollars to repair them. If these aren't in decent shape, it will give problems.
(2) All of the oscillators (or the rollers that are actually "fixed" in to the press) should be in good condition. You might have to replace the removeable rollers when you buy a press, but if you have to replace the fixed rollers, you are looking at a lot more $$$
(3) The electronics should be in working order, such as the ink key controls, etc...
(4) The Plate and Blanket cylinders should not have large gouges or dents in them. Smaller things on these cylinders might be workeable, but large defects in the plate and blanket cylinders can also present a lot of problems.
(5) ANY auto-lubrication feature should be in good working order, such as the oil drip, etc... If one of these features isn't working, the press could already have serious damage accumulating.
(6) Is the press capable of doing what I need it to? You would be surprised how often this is overlooked.
There are a million other factors as well, here are just a few from personal experience. Hope this helps