I'm from another generation remember, and when I was young, guys paid. Period. It was still quite new that women paid for meals, tickets, etc.
I like the "I invite, I pay; you invite, you pay" system in general. This way you can control the price of the bill by choice of restuarant. If she wants to go to an expensive place, ask her if she's paying! If she's not paying, she has no choice in the place.
As for splitting the bill...that's what my girlfriends and I do. If a guy wants to split the bill....he's just became a girlfriend.
I will repeat, for the 1000th time, that the first couple dates should be inexpensive. Coffee & pastry at Starbucks, lunch at a Chinese place, Breakfast at Denny's. If she starts complaining...then you know you have a "Dinner Wh.ore". Dating is about spending TIME not MONEY!