My advice is DONT PAY. You can occasionally pay after you FUCK her already.
First, paying for stuffs and worry that she would think that you're cheap is an AFK mistake. You will appear as trying to buy her affection, and do you think that will make you different from all the other AFCs who hit on her before? NO
Second, once you pay, it will become a habit, more or less of her expectation from you every time you go out. It will be hard to change that later.
If you don't wanna look cheap, there are millions to show her that. (ex: you give waiter big tip after paying your OWN bill, etc)
If you still feel bad about not paying, here is what I usually do: I offer to take turn to pay for the date. Like I would pay for dinner and she needs to pay for the movie, but always take the bigger bill.
Another way to do this is makes her feel like she earned it ( Ex: a bet, a game , a riddle, etc)
I'll give you an idea on this one also. I usually ask the girl out to help me pick a present for my friend, make sure you tell her its for a girl so that's a DHV. ANd you got urself a casual no pressure date. Then later on use this as an excuse: "Hey I wanna thank you for helping me the other day, come to [place] at [time]"
There is your second date, and this time you can offer to pay as a token of appreciation.