On the next date when you buy something like tickets to the movies, just preempt him and say that you'll get it because he paid for it last time. With his response you could go a few ways:
He Says: Oh don't worry about it, I don't mind. / Are you sure? / Cool, thanks
You could respond: It's fine, I don't want you to pay for it, you got it last time. / Sweet
It's all about balance in where you both stand with each other and the situation, it's not that much of a big deal. I know that I do that with friends, one will pay for drinks because it's convenient and the other will get the next round/ shout some other time or I'll bring food and someone will bring furniture or whatever. I don't see why dating a guy would be any different than going out with friends (besides the hopes it will be more than friendship!). It doesn't have to be 50-50 as along as you neither of you take advantage of the generosity.
Personally, when someone offers to do something for me without me asking, I expect that I would return the same courtesy and that is all (not necessarily right away either but in this case I think you should).
The only thing I really remind myself to do is to be attentive to my date and it's pretty easy to do that if I'm into him. Notice how close he gets to me, carry his jacket if he's fumbling around for keys, smile when you look him in the eyes. Little things makes people notice you.
It sounds all so adorable. Hope it goes well.