All combos will suffer from the same problems, chatter caused by lack of stiffness, lack of capacity, etc.
If you do go that way, best to go with a lathe that has a tacked on mill rather than a mill with a tacked on lathe.
For airgun work, you'll get more use out of a lathe than a mill. The spindle bore will be the limiting factor, it needs to be large enough to get your barrel through it. You might want to look at:
and then go with a mini mill:
same mill, but cheaper:
By the way, when you start looking around, you'll realize that there are only a couple of manufacturers in china for the hobby mills and lathes and everyone just paints them different colors.
If you want to be real stud, get an old South Bend, Atlas or Sears bench lathe. I'd still go with a modern bench mill because there just not that many good old ones available.
"Bones heal, chicks dig scars, pain is temporary, glory is forever."