If you're flying in Basic Economy, you'll be allowed to check in for your flight using the United app only if you specify that you'll be checking a bag. You'll need to travel to a check-in counter or a dedicated kiosk in the airport lobby to check your bag. You'll have to finish checking in for your flight at the airport if you start checking in and don't indicate that you're checking a bag.
You will be charged for your first checked bag on trans-Atlantic flights with United Airlines baggage policy economy tickets. Trans-Pacific fares include one free standard checked bag.