Create an ideal customer profile. Create some questions that will allow to you survey a potential tester to determine if they fit your profile. Design simple landing page with very clear value proposition that speaks to your ideal customer.

Ask for a minimum of information up-front (email), but ask for more info after they commit by submitting the first piece of info. (KISSmetrics does a good job of this on their current website trial signup).

Use the their answers to these profiling questions to put the applicants into buckets. Let in the most ideal bucket first, or split them into groups if they're big enough.

Try and measure engagement the best you can. Measure qualitative and quantitative data. Schedule calls with your beta testers to find out more, especially with the ones who's user behavior seemed to indicate that they didn't get value from your product. Find out why. Make sure they are indeed your ideal customer. Pick up the phone and get to know your customers inside and out. Meet them in person if possible. Incorporate their feedback quickly and get more feedback. Rinse repeat.

The first thing you're going to want to do is better "gate" your sign-ups. The fact that you're not trying to learn anything about who is signing-up by either providing different CTA's on your landing page or by offering them a quick survey for faster access, means you won't know which users' feedback is closest to your "ideal" user.

In early experiments I've run like this, we've seen a 5 question survey get between 20-30% response rate as a means by which to get faster access to the product, so absolutely worth doing.

I like to run different types of users through a closed beta. "Patient Influencers" are people who can lend credibility to your business when in launch (either by testimonials, press, access to potential customers or investors) and the other are your most "real" users. What you're most looking to do is collect that product feedback and look for where these two groups' feedback overlap.

I have a lot of experience in early-stage product ideation and guiding it to product/market fit. I'd be happy to give you some more and contextually-relevant guidance in a call.

Do you have specific concerns about running a closed beta, or are you just generally trying to be prepared for it?

Ideally, you would know or seek out an initial group of youth ministers who might be interested in using your application, interact with them directly, perhaps conducting some usability testing in person, but also monitoring their use of the app and continuing to work with them directly throughout the beta.

If you are successful at convincing these ministers of the value of your web application, they will help you convince others, which is usually the best way to grow. You might even select some of these initial customers to join a customer advisory board over the long term if that ends up feeling useful.

If you have concerns about scale, you can always move from a closed beta to an invite-only beta that helps you manage scale, but I'm not certain that's going to be one of your immediate problems.

I believe this link will give you all the help you need: https://medium.com/swlh/how-to-conduct-a-closed-beta-testing-with-zero-budget-acd19c2de43
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath