If you do not specify a password to useradd it won't get set (and the user will thus not be able to log in via password). Note that useradd and adduser are two different commands.
The following should create the new user with its own group, create it's home directory (at the default location, as we do not specify any location) and copy skeleton files.
useradd --create-home <user> Then you just create the directory .ssh in its home directory, chmod it to 0700 (SSH will want this for security), and put the users public key in .ssh/authorized_keys (the private/public key pair should be generated by the user him-/herself, on his/her own computer).
If you want to disable the password of an already existing account you can use the following.
usermod --lock <user>