Depth of hole does not depend on the bit length for a drill press. It depends on the āstroke lengthā of the individual drill press. 3 3/4" minimum would be good for drilling 4x4ās which have actual dimensions of 3 1/2"x 3 1/2" if you are buying the standard treated ones from building suppliers.
Stroke length should be stated somewhere on the specifications for any drill press. Most benchtop drill presses do not have enough quill stroke/spindle travel/stroke length to drill through a 4x4 in one pass and itās not that easy to get holes to meet exactly drilled from opposite sides.
I like to use a Forstner bit, which will cut a little slower than an auger bit, but leaves a nice clean, smooth hole.
Fasten a fence to the table-just use a straight piece of wood-on top of a backup piece of plywood-so you donāt get ātearoutā around the edges of the hole where the bit comes through.
Hereās nice $2500 drill press, but notice that even it has a stroke length of less than 6 inches. For making standards, if you canāt punch the holes in one stroke, I wouldnāt bother with investing in a short stroke drill press, unless you had other good uses for it. http://www.ellissaw.com/Drill-Presses/43/drill-press-9400