I would recommend a cheap set from Harbor Freight or equivalent, and use the same drill bits for metal or wood, except for some wood spade bits. Most of the time, drill bits will fail in a hand drill because 1) the rpm is too high and overheats the cutting edge in metal, or 2) due to lack of control and the tip snaps when exiting the far side of the material or 3) from wobbling/buckling when putting load on a small diameter (<1/8") bit.
Unless you're drilling hard steel or stainless, cobalt won't matter and HSS should be fine. Split point tips are fantastic though (less force needed and won't dull as quick) and recommend a set like that, at least for bits less than 1/4". Anything bigger than 1/4", you should be drilling a pilot hole anyway, then enlarging to the final size.