Maybe easier to go to xbox.com and sign in using your live account and it will show you your avatar and friends list so you can add and authorize friends from there etc.
It's sometimes just a little easier to set everything up from your PC to begin with although you strictly don't have to.
Xbox 360 - Official Site - Xbox.com
You don't need a cosole at all. Your WP7 will do just fine for your friends list. :)
They add your Gamertag, not your email address. You only pay if you wish to play online with the console using the Xbox Live gold service. Your friends list is still free with the normal unpaid (Silver) service.