We did a private beta when launching Honeybadger.io, and it worked really well. We reached out to people we knew who would be good customers, had them go through the same signup flow we planned to use after launch, and had them enter payment information and get billed (so we could test everything). We offered these first customers a special, low-priced plan as a thank-you for helping us test the product.
I think it would be fine to do manual invoicing for this group of customers if you don't have your credit card processing in place yet. These first customers should be ones who will understand that they are testing, so not everything will work. On the flip side, though, you should be prepared to offer them excellent service, responding quickly to any issues they encounter. These customers can become a great source for referrals for additional customers if you treat them well, so treat them well. :)
I think it would be fine to do manual invoicing for this group of customers if you don't have your credit card processing in place yet. These first customers should be ones who will understand that they are testing, so not everything will work. On the flip side, though, you should be prepared to offer them excellent service, responding quickly to any issues they encounter. These customers can become a great source for referrals for additional customers if you treat them well, so treat them well. :)