Upvote:2
I wouldn't depend on being able to show a screenshot stored on your phone, things can go wrong (phone dies, etc.). You should always print these booking confirmations from the website you booked on.
There's no single answer to the next part of your question, and really depends on the discretion on the officer. If you have some accommodation booked, show proof of it. You'll also need some bank statements (again, printed) and/or credit cards with you to show you will have sufficient funds for the duration of your stay and explain you'll be couchsurfing.
Upvote:7
Booking.com provides printable booking confirmations which, once printed, look much more trustworthy than a screenshot. I always carry these when I go abroad.