I would wait for him to contact you again. Let him take the lead for the first couple of dates. I want to see that he is interested enough to put some thought and effort into me. You can tell a lot about a guy by his contact. Does he establish regular contact? Is it overwhelming--like multiple emails and texts every day after one date? Does he wait a week? Does he plan something interesting? Or does he call you up the day before and want to hang out? These things all give you some clues.
If you take the lead and contact him now you set a pattern and show him that he doesn't have to do the work or plan.
Again, this is just for the first 2-4 dates. After that, you should feel comfy enough to contact him whenever--even if you aren't exclusive.
I also suggest taking things slow. If there is a connection, there is a tendency to have high contact. Lots of emails, texts, and calls in the beginning can create what I see as artificial intimacy and lead to high expectations before you know them. You don't have to call. email or text back right away--savor it. Take some time and have a bit of mystery. Being too available isn't attractive--it can come off as needy.
I have asked men out before and actually asked my ex to marry me. So this isn't about being hung up on gender roles. I've found that I enjoy being pursued a bit instead of pursuing. It's really a nice feeling to know a guy is "into you".
Also, search "red flags for dating" just so you are familiar with some of the big ones.