Once things are stable, start scaling the beta up to a reasonable number of users. I.e., stress test, in increments. Once you meet a pre-set milestone, set it loose.
Goodluck!
Frankly, I think you'd be more than fine if you let it be on a first come, first served basis, with the added caveat of garnering a little market research. That way you're not turning away too many people.
You run the risk of taking on a lot of work if you start filtering everyone. And if you do that, you may miss out on a potential market you hadn't identified previously. Just a thought :)
It's more focused on desktop apps, but it has good insights