chuck fitting

While investigating excessive runout on my new-to-me but old-to-the world drill press, I noticed some runs of epoxy around the top of the chuck's taper adapter.... Removing the chuck was not fun but I eventually got it to release. Some previous operator had slathered the taper in epoxy then...

I recently bought a "Set-Tru" type ER-40 chuck with D1-4 camlock mounting. With the studs properly adjusted the chuck does not flush against the lathe spindle. The lathe spindle checks very true. The instructions say to shim the chuck back plate to the lathe spindle if needed. I don't want to go...

Obviously, I'm a beginner! And this is a very beginner question! I'm looking to purchase a four-jaw independent chuck. How do I make sure it will attach to my machine? I've searched this site, as well as spending some time on that other forum where hobby guys are not as welcome... I've seen...