This is a toughie. Tons of single people—most, I'd guess—are single by accident. Unlike your partnered friends, you just haven't met the right person at the right time, and that's no reflection on you.
Unless, of course, you really do have a problem being too pushy with potential partners, smothering them in an attempt to nudge along a relationship. If you are not sure, ask a (female) friend of yours to honestly tell you what she thinks.
But either way, I think the "letting it happen" thing is both right and wrong. In terms of the pace of a relationship, yes, please let that unfold naturally. Don't push too hard to move things along.
In terms of getting dates, though, like actually locating the people that you go out with, I think it is great to be proactive. Especially if most of your friends are partnered, how are you going to meet single people unless you try? People roll their eyes, but the internet is your friend. I know many, MANY people who have had great luck finding both flings and serious relationships online, especially in the city, where it is hard to find appropriate ways to approach people you think are cute, but do not know.
Good luck out there, man, and don't stress about it too much: active searching is great, but people can smell desperation.
In your opinion, what is a healthy or average number of sexual partners a single person in their early thirties should have? Or in other words, what is a number range that most women wouldn't find either "too inexperienced" or "too alarming"? I have only had one sexual partner (long term relationship that ended years ago), and the women that I become interested in seem to express their concern over this.
Oh my my my. The old "what's your number" thing. Nobody wins that game. One person feels slutty, the other naive. The whole revelation injects this totally unnecessary amount of thought and meaning into something that is not that big of a deal, given that we are all adults here and not from some dumb show about shoes where sex columnists can afford apartments in the West Village.
Is one partner low, on average, for a person in their early thirties? Yes. But you know what? Who the fuck cares? Seriously. I would find it way more "alarming" to learn that my boyfriend had only fucked one person, then went out and joylessly fucked a bunch of other people solely in the name of sex number correctness.
So my advice to you—and to everyone really—is to refuse to participate in the number conversation. It's nobody's damn business. "I really prefer not to talk about that." That's all you need to say. Plus, extra credit, now you seem classy and mysterious.