Originally Posted by
McCreed
Just to expound on what Andy said, a critical measurement on a drill press is called "throat depth". This is the distance from centre of chuck (ie: drill bit) to the vertical post that the table and motor are mounted to.
A lot of manufacturers label their machines with "swing" which is 2 x throat depth. For example my drill press has a 325mm swing, which equals 162.5mm throat depth, and is just deep enough to comfortably do a standard strat or tele body string-through. IIRC, a strat requires about 158mm or so.
To buy a mid-range quality drill press big enough for this will likely be a minimum of $400. You can easily drop $800 on higher range ones, so "cheap" is dependent on the size of your wallet. I think my Trademaster TD1316 was $479 at the time.