The problem I'm running into is that I wouldn't know a good(or bad)
deal when I see one on a machine like an old Atlas mill or Atlas lathe.
And there seems to be little info on these machines on the internet.

I have not been following this thread so forgive me if I repeat something.

It appears you are a beginner with limited funds living in an apartment.
I think you should look at the import 7x10 or 7x12 mini-lathes. They
are small and reasonably cheap and will get you started. There are lots
of web sites out there showing how to improve these machines. If your
projects are small you can look at sherline too. They are a good way to get
started but you can spend a lot of money on them and you might outgrow
them quickly. Another good option is the import 7x20 lathes but they
cost a lot more than the 7x10 minilathes

I have owned several atlas/craftsman lathes and mills. I didn't care
much for the atlas horizontal mill and would not recommend it to a
beginner. The atlas lathes are ok but not nearly up to the level of
the bigger machines like logans, south bends, clausing etc. Bruce,
one of Dick Trimstra's friends specializes in restoring atlas lathes
and I have seen some beautiful 6 inch atlas lathes for reasonable
prices. Even for a 6 inch lathe, you will need to dedicate a fair
amount of room for it. You can stuff a mini lathe or sherline into
the closet if you chose.

My favorite small lathe is the myford super 7, but its probably
out of your price range.