Make sure it has more than a 2" travel. I am having a hard time drilling blanks on mine because the bit is so close to the tray.
I had the Harbor Freight bench top drill press with a 2" travel. I learned to work with it because it's what I had. That meant that when I did a longwood slimline, I had to set up and drill four times for one blank. Was it a hassle to do this? Maybe, but I made three or four, and always had to drill at least twice per barrel no matter the pen I was making.
I traded that one in and upgraded to a drill press with a 2 3/8 Spindle travel, and it make a big difference. The only reason I settled for a mere 3/8" more was because I was using the HF service upgrade, and that's as good as it gets with their bench top models.
It can be done, but shop around and find one with at least 3". There are ones out there with much more. Four is better, six even better than that.
Be patient and don't forget Craig s list. If your buying used, take along a bit or straight rod to check for run out.
ETA:
Forgot to mention that you should also check for distance between the chuck, and table. One of the reasons I had to drill four times for one longwood was because I couldn't start with the table, and had to use the base because there just wasn't enough room between the table, and chuck. My first one only had 7" (IIRC), and when you put a bit in that doesn't leave much room. 3-4" spindle throw would have been a joke with that much limitation between the two.