Are you presently drilling with a hand-held drill and now want a drill press, or have you not yet drilled any holes and just think you will need a drill press.
If it's the second case, try using a hand-held drill with standard HSS bits first, for most hobby purposes it will be fine, either with a dremel (probably the flexible shaft might be easiest) or with a small DC motor and collet chuck, example:
http://www.ebay.com/itm/12V-Smaill-PCB-Drill-Press-Drilling-Motor-w-0-6mm-0-7mm-0-8mm-0-9mm-1-0mm-1-2mm-/231025746719I use the motor and chuck hand-held, I can drill pretty quick, maybe 2 seconds per hole on average, with a 24v motor ripped out of a printer. Fairly accurate provided the pads are center etched to locate the bit. I use 0.8mm and larger bits.
If it's the first case and you've had enough of hand drilling and want a press (or want better accuracy), then as above the Dremel press doesn't have good reviews, too much slop. You also need something that can really spin fast to make good work of the holes with our small bits. Runout must be almost none (especially for carbides, HSS is not so much a problem, again as long as the pads are center etched).
The type of drill in Fran's video is often seen on ebay (and aliexpress etc) out of China, she does mention she had to mod it to improve runout but I don't think she went into details how, perhaps contact her and ask.