OK, I'm the last person who ought to offer dating advice because I've been happily married for 40 years, but I have heard an earful over the last decades from my sons, my friends, and my students about what it's like out there these days in the dating world.
For what it's worth, I'd be predisposed to think of your meeting as just that--a meeting to see if the two of you have a mutual sense of connection when you are face to face. After a few minutes, if you aren't relaxed enough to enjoy the conversation, or if you aren't feeling positive about the person, I'd be inclined to finish my coffee/drink and make a graceful exit. I'd also be leery if I didn't sense the connection was mutual. Personally, I wouldn't much care to spend time with someone with whom I couldn't relax enough to be myself. And I'd want to be interested enough in that person to find out more about their likes, experiences, and opinions. If half way through the meeting, I was still thinking about my appearance or struggling to find a topic of conversation, I'd be seriously questioning the point of what we were doing.
From what I've seen being the only woman in a houseful of males, my own observation is that too many woman seem to feel it's their role to make relationships happen and that males are naturally disinclined to do much of the work. To be honest, I hated it when my sons were dating women who were obviously investing much more time and effort than my sons were in the relationship. I know for a fact, when my sons were interested, their attitudes and actions definitely were driven by the desire to make the women feel desired and appreciated.