Dating hasn't changed very much in the past several years (I'm a single Mom who is back in the dating scene now). Being yourself is the best route. Don't talk about your marriage or ex unless she brings it up. A lady wants to see you've been able to move on from the past.
Also, you might want to consider a Parents without Partners group. Its a way to meet other single moms and dads in a no pressure situation (I should listen to my own advice on that one, lol)
Kissing-for a first date, a nice firm kiss on the lips if she doesn't turn her cheek or a smooch on the cheek is nice. Hugs usually work well too.
I imagine you will get other advice. If you want to commiserate, feel free to pm me. Dating is never easy, especially in our situations. Best of luck!!
hugs
I'm not a lady, but I've seen a few of them say something like this: you might get more responses if you put some more info re: your interests, etc. on your profile. good luck.