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The Innocraftsman chucks have a minimum closing distance of 0.3 - 4 mm for the universal chuck and 3.175 for the collet chuck.
This minimum closing distance of the collet chuck is equivalent to about 1/8" and will only hold the shank size of the commonly seen short carbide bits used for drilling printed circuit boards.
If my calculations are correct, the Innocraftsman universal chucks will not hold HSS bits smaller than about 1/8" (0.125") or above a number 34 numbered bit nor larger than about a 5/32". To use a HSS bit smaller than a number 34 in the Innocraftsman chucks, a bit holding adapter will be necessary. The usual numbered bit indexes modelers commonly use contain numbers 61 through 80.
Paying $129.00 for a drill press with such a narrow range of drill sizes would be a deal-breaker for me. Your mileage may differ, of course.
View attachment 540111
I think the chucks on most of those drills mount with a JT0 Jacob's taper. Keyless 0-3mm chucks are available, but cost around the same or slightly more than the drill itself. However, it may be worth it for the additional range.