Do it "right" depends on the what you're comfortable with. Being a practical guy, I don't see a huge problem with seeing more than one person casually, or even semi-seriously, as long as it's understood by all parties that you're just seeing each other and there's nothing exclusive. The "practical" aspect comes in because I like to maximize my chances. If one girl ends up not working out, there's always the other(s).
But that also means juggling schedules and keeping track of multiple sets of interests and priorities and all that. You definitely do not want to find yourself asking your date how something turned out, you know, that thing you talked about last time, only to realize that it was a different girl and you got them mixed up for a minute. So I can see why, as a rule, some guys prefer to keep things one-on-one.
The important thing is that you're back in the game and sharpening your skills. Yes, that makes it sound rather impersonal or something, but as I said, I'm a practical guy, and this is something which often requires some thought and review along the way. It sounds to me like you're doing fine.