HB, I haven't dated in awhile, but let me dust off my ol' dating brain. I think dating do's and dont's are confusing for everyone these days!
But when it comes down to it, I think men and women are still kind of old fashioned.
I play it safe and bring enough to cover the evening. But I am definitely still old fashioned. Not all dates go well

but even then, I recall the man taking care of the check. I always offer though to go 50/50.
Generally for me:
If it is a first or blind date initiated by him, he picks up the tab. If I ask someone out, it is usually someone I know, and I always offer, but they will get the check (esp if he is interested).
If we go out again, he gets dinner, and if we go to a movie, I always offer to get the popcorn, soda, etc

if it is out for a nightcap, he will get it. But I offer.
I usually do not invite a man into my home until later in dating situations (for instance, to make dinner for them or to watch a movie), because in my experience, most times, they take it as an invitation to stay or as an invitation to make out, and if I am not ready or interested in that, it can be awkward.
If he asks me to his home, I call my friend and tell her/him exactly where I will be. And when go there, I bring a bottle of wine or a small dessert. As the evening winds down, I have the option to beg off (if I am not ready or feeling it) and will take myself home.
Some may have a different approach and/or disagree...I know there are different POVs on the whole dating thing
Whatever the case, if you are having a date, have a great time! Have fun!