Asking a guy friend on a coffee date?

My guy friend and I admitted we liked each other at the end of last semester, and decided to think things over during the summer. Now that we're back at school we have mostly been hanging out in groups and flirting a little, but there hasn't been any sort of "defining the relationship" talk. I know that I want to take it further than just friendship, but I can't figure out what he wants.

Rather than put a lot of pressure on him by confronting him directly with scary questions about Feelings, I want to ask him to go get coffee so we can catch up and unwind, and hopefully then more dates and maybe a relationship will come. I don't know how to handle this though! I can figure out how to do the asking - it's just everything else that is confusing me, like who pays? How do I establish that it is more of a date and not just a chance for us and ALL of our friends to hang out? What day of the week/time of day is best for a coffee date? What if he doesn't even like coffee? Is this all a horrible idea?

It's been ages since I've been involved with someone new, and I've never done this formal date-asking thing before. Help!