You absolutely need to meet each other!
However, I don't think that it should be a "meeting" between the two of you exclusively, because then that just creates a serious atmosphere that invites deep discussions, which you DON'T want when you're first getting to know each other.
Instead, you should both be attending your children's events (sports, b-day parties, etc) and you can all sit together. Then you can make some conversation with each other but not feel forced to have to talk the whole time, since you can focus on the kids' activities. The kids will see you two talking and playing nice and that's good.
You two don't have to be friends, but you should at least know something about each other and your views on parenting.
I am a step-mom and I sometimes sit and hang out at my step-daughter's mom's house for half an hour & chat with her mom while I'm picking her up or dropping her off. It's very easy-going and we can fill each other in on important things that are going on with the child. However, we don't talk about our personal financial issues, marriage issues, etc. like we would with close friends, because that just provides "ammo" if something ever goes wrong.
I wish you luck.... I'd really just try and convince your ex's wife to attend the kids' activities and take it from there.