Rebooted the system and up came Ubuntu Login:

During installation you should have been prompted to create the first user. That's the username you should be entering.

'Password' appears, but it won't let me type anything?

That's because Ubuntu won't show the password on the screen (even as you type it).

If you can't remember your username or password, then you need to boot into recovery mode as described here: How can I re-instate my admin privileges?.

From there, you should be able to add a user account (and set its password) for normal use:

adduser myUserName

Give it a password and provide any other info asked.

Adding user `myUserName' ...

Adding new group `myUserName' (1001) ...

Adding new user `myUserName' (1001) with group `myUserName' ...

Creating home directory `/home/myUserName' ...

Copying files from `/etc/skel' ...

Enter new UNIX password: 

Retype new UNIX password: 

passwd: password updated successfully

Changing the user information for myUserName

Enter the new value, or press ENTER for the default

    Full Name []: tester

    Room Number []: 

    Work Phone []: 

    Home Phone []: 

    Other []: 

Is the information correct? [Y/n] Y

Then, add this user to the admin and sudo groups (assuming that you want your user to have the ability to "sudo").

adduser myUserName admin

addgroup myUserName sudo

Or as Rinzwind suggested, check the /home directory for any existing users. If you find one but you're unsure of that user's password, reset it:

passwd myUserName

Then reboot and login as your new user.