Should the man pay for a coffee date?

I asked a woman out on a date (in person, not some stranger I met online), and she suggested coffee. Most of my first dates have been dinners, and I've never done coffee as a first date. I presume these are just pay at the register, not table service like restaurants. What do women expect for a coffee date? Should I wait inside for her (assuming I arrive first) then order together and pay, or is coffee considered casual and cheap enough where it doesn't matter?