Yeah, from my perspective, alternating paying is a decent option if you'll be seeing each other for a bit.
My purse likes it when a guy pays, but at the same time if I do not know the guy well, I do not like the feeling of obligation I sometimes get if a guy has been shelling out all the money; it can leave me feeling like I need to compensate with something else, regardless of what it is. I don't like obligations.
If the guy asks me out to a nice restaurant, I expect him to pay. [Rule: If the person choosing the place for the date chooses something 'expensive,' they should offer to pay; and if they don't, the other person shouldn't accept the expensive place if they don't want to pay their own way.] If he says, "Hey, let's do coffee," or "Let's just hang at a fast-food place for awhile" ... so it seems casual and less "date-y" and the price is cheap, then I expect myself to pay my way. But overall I tend to feel it out and go with what seems appropriate based on context.
I would never initiate a date and/or choose the place and THEN expect him to pay for both of us, unless he specifically says so. And as far as etiquette, if we're someplace where I thought we were going dutch and he offers to pay or just goes ahead and pays, I always say, "Oh, you don't need to do that," and then if he comes back with, "No, I'm going to / I want to," then I just go with it graciously.
I just don't ever want to be seen as a gold-digger/freeloader type, but I've learned to accept a gift when it's offered.