That's exactly what we use at work. A laptop with an external screen.

Your questions:
1. We have 23" or 24" with a normal HD resolution (1920x1280). Works fine for me. You'll have to try what suits you.
2. Most monitors are matte (like most LCD/LED TV's).
3. It's nice to use an external keyboard also, so you can move the laptop out of the way. And you might like that the screen is on the same height as your eyes.