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.Â
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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.Â
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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.
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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.Â
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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".Â
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Also, search "red flags for dating" just so you are familiar with some of the big ones.Â