You're supposed to win by landing the guy you want, by being the woman he's looking for...same as the rest of us, ultimately.
How can I be what someone else wants, while being me at the same time - something that's within my capacity to be, and is also genuinely me, my real interests thoughts and feelings - it's a question I think a lot about, all the time. It's a hard question and the world doesn't help things.
"For what"? Just to get the whole process started. Not even to be your friend but just to see if you like each other's company enough at all to want to see each other again and keep talking, keep getting to know each other. The more casual a first date is, the better, I think. It takes a little while before you find out if this person is someone you can move forward with so I think the focus should be on things like, is this person interesting enough, do you like them enough as a person, etc. You can get into the formal stuff later after it's established that you're going to give each other a serious try. Having to do all that formal stuff too early adds more pressure on top of an already stressful situation of just trying to make a good enough first impression.
All of that "I bought you a meal, now you owe me", "friendzone" stuff happens, I think, when one person decides the other is not the kind of person they're looking for. If everyone pays for their own meal, then you can both focus on if you enjoy each other's company or not.
Sometimes it's an honest mismatch, but sometimes I think someone makes a bad impression out of not knowing any better, not knowing how to play their part right, not being where they should be as a person, and things like that where it didn't necessarily have to end that way.