I've built an MVP and have about 35 beta sign ups. It's not much but my landing page conversion rate is fairly high so far, so that's a good sign.
I've sent out about 10 invitations to sign up. Half of them signed up and used the app. I did some background research on the sign up emails and initially invited people who didn't seem to be my exact target market. Reason being, I wanted a few people to just go through the sign up and setup process to make sure they didn't run into any major bugs.
The remaining 25 sign ups are in my target demographic. I'm hesitant to invite them because I feel the product needs some improvements.
My gut tells me to throw a red flag out and get a feedback ASAP from these users. If I were giving advice to someone else in my position, I would say stop what your doing and get feedback.
I think the root of my hesitation comes from me being the sole founder/developer/designer/growth hacker/etc. I have to labor for every site visit and sign up at this stage.
Some of the qualified sign ups are even openly enthusiastic about my product on social media. I feel if I invite them now, I might lose out on the chance of turning them into product advocates.
No product survives first contact with the user base, so even with further improvements and refinement, it's still not going to be exactly what they were looking for.
Just tell them it's still in development, and as early users, you'd really like to get their feedback to help shape what the product should be. They'll come in to it knowing that it isn't complete, and early adopters like these people (I assume they're the early adopter type) are used to products that still need refinement. If there are any huge showstopper bugs, fix them (don't give them a broken product) but don't worry if it's not "finished".
It all depends on the size of your target market.
If you have thousands or more of prospective users, just on-board people as fast as you can keep up with. You don't need to know how cool your product is, you need to know what's not working for people. The more users, the faster you can learn, and the easier it is to choose what to prioritise.
But if your target market is small, you may not be able to afford to work this way. The leading alternatives I've seen used well for this case are:
Good luck. Most people never get their product beyond their friends and family, so you're already doing great!
@rbwhitaker hit the nail on it's head.
You should get as many people to use the beta product as you possibly can. Don't worry that the initial users will think the product is subpar.
Mention to them that it's still in beta and they're one of the few people getting a preview while you're continuing development of the first official release. Most users feel good about being early adopters and will help you evangelize your product if they get any value from it. It play's into our human nature of being seen as on the cutting edge.
I'd also recommend getting feedback with direct communication (in addition to the app's usage you're already analyzing). The best time to reach out is often after their first interaction with your product.
StatusPage.io did this well when they launched -- they sent a short email after a new user completed a basic first action. And asked if they can help the user further use their product. This helped them figure out some of the pain points in the user experience.