Men in their 40's or 50's please answer.?

I am a divorced 50 yr old women and would like to start dating. My 3 sons, in their early 20's tell me that women should pay for their dates. I tried this with someone I was seeing and it was offensive to him. He knows I am temporarily financially challenged at this time. I don't want to be a freeloader or take advantage of anyone and need advise. What is the proper etiquette for dating these days? Who is expected to pay for what, is it a 50/50 split, do we take turns buying? What is the right thing to do?