Yahoo mail is mostly used by business man before so it's security is little bit tight compared to gmail.
Sometime Google doesn't required phone number specially when the phone or computer is new, you can create maximum of two gmail and you don't need to used phone number to verify but for the third time and more they will request number to send the verification code.

Gmail is surely created and valid when you read the inbox saying welcome!!!!
So you don't have to worry anything.
Just to make sure you out some extension email or phone number to your gmail incase you forget your password.

It's ideal also to put up your personal questions because people tends and try to open your email and sometime it locked out.

Carefully review gmail notifications about your email opening to other device.