I see that your site is now in public beta, but since you asked about private beta I'll talk about both phases.
I've been involved in the private-beta phase of a few Stack Exchange sites, and what I've seen is that for private beta, your focus should be on people who are already users on other SE sites. As you're working out initial scope and that crucial first set of questions, it's important to have people who know how SE sites work and what kinds of questions will flourish. You need some of them to be experts in your topic, of course, but an SE-experienced hobbyist beats a high-level expert who's never used SE before, at that phase.
This continues to be true in the early weeks of the public beta, but once you're public you can more-easily reach out to experts who aren't already aware of your site. As with any recruiting task, this seems to work best through personal contacts.
There's something of a chicken-and-egg problem, though; you need experts, but experts need to see expert content. Don't rely too much on recruiting "outsiders" early on; your primary goal is to strengthen the community that's already there and broaden its reach. The people you already have have invested in the site, and you can help them continue to do so by actively engaging with them. Answer their questions, leave comments on questions and answers asking for clarifications or expansions, direct people to relevant meta conversations, inhabit your chat room, vote, highlight good contributions (everybody likes to be complimented)... make it easy for people to feel part of the community and not like they're just sending their posts into the void.
New posts, in particular, should get prompt attention. Are they good? Upvote! Can they be improved (and you know what's needed)? Edit! Can they be improved, but only by the author? Ask a question in a comment. Can you answer? Then do that. If somebody asks a question and then gets no response for a day or more, he's probably going to wander away. If somebody engages with him promptly, even if it's to say "err, there's a problem", you can start to build that connection.
I also agree with this answer: reach out to your key users who are already established users on your site. Building a site in the first month requires a different kind of participation than helping to sustain an established, years-old site; some of your users just want answers to their questions, but those key influencers want the site to succeed. Help them help you do that.