My cheap import floor model drillpress has very noticeable runout on the spindle which is bothersome sometimes. Most of the time it doesn't make any difference unless I have a very small drill bit in the chuck, then almost invariably the bit breaks. So look and feel for any wobble, wiggle, or shake on the chuck.
Most DPs have some type of depth stop, which is very handy sometimes. Usually a locking knob on the quill feed,
Don't throw away the old tabletop, if it's any good. I use mine with an 8" disk of MDF chucked in it, charged with white polishing compound on the top face AND edge, to hone all my edged tools (kitchen knives, lathe tools, etc.) The top face is great for the skews especially.