jives (OP),
What is the size of your drill press?
They're several ways to skin a cat, its just matter of finding which way you like to do it? I have drawers of vises (I use to collect) including Kurt, Starrett, Brown & Sharpe, Heinrich, Palmgren, Cardinal....etc
One common thing that I think we all can at least agree on is the ease and speed of clamping down the vise in place is very important. A vise that's hard to clamp down to your table or takes a while, will most likely be used without being clamped, Rambo style.
I recommend a vise (whatever it may be) that it has bolt down tang slots on the sides or front & rear or both like a Heinrich. Personally, I use two hold down vise grip style clamps mounted to my DP table that is holding my speedy vise for a lot of the time. I can position it almost anywhere on the table quickly clamp it down, quickly re-adjust it, if needed. For big work or critical, then bolt down. Also good for holding items without needing a vise.
Having a good flat smooth DP table is very helpful, having a vise with a very flat, damage free bottom is also key so when your moving it around on your table, it's not damaging it and staying perpendicular to the drill bit.
Heinrich's are great vises and was mentioned in my link above but for some reason, I keep going back to my Speedy (holds great and less knobs, lower profile).
Another recommendation, for putting holes in small items, I usually hold them in a small 1" toolmaker vise (like Brown & Share 752) with no bolt down tangs and then clamp that to my regular drill press vise and any orientation. It make things so much quicker, I can set it up on the work bench, check everything and then take it to the drill press and then if needed I take it to my bench vise to hold it if needing cleaning up or if needing a tap or whatever. You can find overseas ones for cheap. It's just a suggestion