The Cadillac of American lathes was either the American Pacemaker, or the Monarchs, and I'd lean towards the Pacemaker. These machines were built to very exacting standards, they were built from very high quality materials, with exceedingly good bearings in the headstocks. If I could find a Monarch 15" lathe, I'd be on it like stink on a cowpie. They're awesome lathes.

For a gunsmith, I think the Clausing 5913/5914's are pretty nice lathes. The South Bend "Heavy" 10 (aka model 10L) is a good (and almost too-well-known) gunsmith lathe. The 10L is very short through the headstock, which makes it easy to put a barrel through the headstock for chambering or threading. The 10L is also a rather light lathe, making it easy to move in/out of tight spaces (basements, workshops, etc).

For many farmers who want to tinker with guns and make parts for farm equipment, I'd recommend looking around for a South Bend "Heavy 13" lathe. These can be found with 60" beds, so you can work on longer shafts and such. The Heavy 13's only downside is that it is low - tall men will end up stooping over the thing and getting a backache, or you'll end up building up a platform to raise it by about 8 inches. But they're a very good "all round" lathe, with very reasonable prices in the used market.

For people who want/need to make lots of little screws/pins/bits/bobs, the Monarch 10EE and Hardinge HLV-H are the ticket. These lathes were used to make very precise workpieces - the bearings on both of these lathes were significantly better than the bearings on most all other lathes; the 10EE's TIR (total indicated runout) was 50 millionths of an inch, and the HLV-H's bearings were good for 25 millionths of an inch TIR (that's 0.00005 and 0.000025" respectively). Most lathes have headstock bearings that are good for 0.0002" TIR - and that includes modern CNC lathes as well.  Neither the 10EE nor the HLV-H (or the even more useful variant, the HLV-H-EM, which had English & Metric thread gearing) will come cheaply. If I saw either one listed for less than $9K, I'd ask "What's wrong with it?"

To be able to have a three-jaw chuck with no runout requires an adjustable back-plate. There are chucks called "Adjust-Tru" chucks that are three jaw (or six jaw) that then have two additional screws on the backplate to allow you to take out all the runout - so you get the best of both worlds: a scroll chuck for quick chucking/unchucking, and the accuracy of a four-jaw to dial it in to perfection. In my shop, I use the four jaw chuck 95% of the time, a collet holder 4% of the time, and a three-jaw 1% of the time.

Where you are in IL, you're so much closer to good, used American machines than we are here in Wyoming. Here, I can locate a half-dozen used lathes that you could use to turn a 25" diameter axle shaft, but it is very, very rare to see a lathe smaller than 15x60" come up for sale. 

BTW - if people have questions about "how to do XYZ?" on a lathe, please ask and I'll try to answer. There are at least three different ways to do most any gun work on a lathe. Too many people tell you "you have to do it THIS way" and that just isn't the case. If I could have only one machine in my shop, it would be a good lathe. A mill is optional most of the time - a lathe is not.