Sorry for not seeing this sooner. Hope you got things figured out or came up with a plan B last weekend.
Check-in has a lot of flexibility, however it also means there are a lot of settings that have to be 'just right' for it to work.
First question: what are you using for criteria? Do they need to be a member of a tag or group ("membership required")? Or, are you using an age, grade, OR birth date range? I would suggest only using one criteria for each attendance type.
Next, I would check on the check-in start and end times for your occurrences. I would keep these pretty broad. If the check-in start time is 9am, it will not let someone check-in at 8:55. The "Monitor" page can be a good place to trouble-shoot this. If you don't see your current occurrences here, something is wrong with the check-in dates or times.
Then, I would probably check on locations. This is set on the attendance type and the occurrence and needs to match the kiosk.
If you see "no classes available" then at least the phone number search stuff is working properly, so that's good. If they can check in but don't get a label, then there's other things to look at, including label settings on the attendance types or printer settings on the kiosk.
I would also try making occurrences during the week and test things out.
There's some of my random check-in tips. Hopefully there's something helpful in there. I also have some report grid queries that I use to make it easier to glance over lots of these settings at once for upcoming occurrences. Let me know if you like that code. Arena Support has helped me troubleshoot check-in as well.
Keep us posted on how it's going.