What to check
Whether the text arrives, how long it takes, and whether the wording displays properly in that country.
Also check that your phone field accepts that country's number format.
Keeping costs down
Numbers that never got a code are refunded after 20 minutes, so finding countries where your texts fail costs almost nothing.
For your own app, which won't be in the list, choose "Other app".
Longer testing
If you'll sign up and log in on the same number many times, use a rental number. Every text during the period is kept.