Wow, this is a really fascinating discussion.
It's something I've thought a lot about, as a very feminine woman, but also as a huge feminist. I've often asked myself, "To what degree are gender roles involved in dating? To what degree
should they be involved?"
For example, I think it's pretty unfair to assume that the more masculine person in the relationship should pay for everything. The rule I always go by is whoever asks out the other person should at least offer to pay on the first date. I think that's a nice gesture to show someone you value their time. But afterward, on second and third dates, things should be a bit more equal, like "Oh you got the cab, let me get the drinks!"
Because in the same way that femmes (and straight women, too) don't like to feel taken advantage of for sex, butches (and masculine folks more broadly) don't want to feel taken advantage of financially (I would assume.)
On the other hand, I have to say that as a femme, some of the dynamics of a date are inherently related to gender. So, in the interest of trying to help atomiczombie, here's a little list of things I feel are important:
1. Respect and attention - I don't mean to be redundant, since a lot of femmes have already mentioned this, but just turning your phone off and being present during the date is essential. I think the most valuable thing you can offer someone is your time and if you're constantly texting, that's a big red flag!
2. Honestly some chivalrous stuff like holding the door open for her doesn't hurt. Part of me wants to say that's some archaic heteronormative bullshit but the other part of me loves it!! Why is this so attractive?? Someone needs to answer that for me :P
3. Maybe the most important component is planning a date according to your date's interests. I once had someone take me to a sushi place even though I'm vegetarian. It was awkward and I felt so bad for not eating anything!
4. Just make it clear that you have a real interest in getting to know her as a person! Like you mentioned, don't dominate the conversation and don't ask invasive questions.
5. Like everyone else is saying, don't worry too much about money! Some of the best dates are cheap - like picnics. I've always wanted to go on a hike for a date, but maybe that's a better second or third date idea, once you get to know each other a bit more.
I hope this was at least somewhat helpful!! Just don't worry too much and try to have fun!