Divorce or Get: Which Comes First?

I am getting divorced, and I’m discussing getting a Jewish divorce (get) with my husband. My question is, does it matter whether the civil divorce comes first?

Jewish Divorce

I am divorced and interested in remarrying one day in the hopefully not-too-distant future. My ex-husband is not religious and not too interested in doing a Jewish divorce, since in his eyes the secular divorce we had is sufficient. If I told him it’s very important to me, he would probably do it. I’d rather not go there at all if I don’t have to. In this kind of situation is it enough to go to a rabbi to get his blessing to get married or is it necessary to do what it takes to get a Jewish divorce?

Cohen and Marriage

Why can’t a Cohen marry a divorced woman? Is she less than others because of her unfortunate situation?