Did he really spell out all three options?
If so, I'd go for the drink.
Coffee could imply a short meeting, especially once you've both finished your coffees, as it signifies the 'end' of the meeting. And no one ever orders a second coffee. Probably a non-issue in the grand scheme of things, really, but still. And again, depending on what time of the day you meet, there could be implicit timing guardrails.
Lunch.. I'd just avoid. Food, chewing, etc. get in the way.
Beers are the best. They're after work and you have the lenience to have as short or as long of a conversation as necessary. You both can drink your beers at your own pace and order as many as you want. Plus, he'll probably be inclined to help you even more if he's buzzing a little bit and you guys have built up a good rapport. Being able to share a beer and good conversation with another man is a lost art (blame the smartphones).
Oh, and definitely insist on paying for whatever you end up doing. If he refuses strongly twice, then relent and let him pay.