I'm actually not sure that it's ok that we are having this discussion in 2015. I mean come on, we're supposed to be cruising around in flying cars and the fact that the physical-paper business cards is a topic today is sorta lame. In any case, the question here is whether it's important or not.
Yes. Absolutely. As digital as I want everything to be, paper-based business cards are still very important, especially at the approach or first time you meet someone; especially a prospect.
Gloss finish or Matte?
I think it depends on the design BUT I kinda think that having a nice glossy finish is never a bad thing. If I were to have to choose, I'd pick a gloss finish.
Biz Card Vendors
These are a few that I have used:
3.5 x 2 inches
add .125 of "bleed" and it should be saved in CMYK mode.