The company that provides your broadband connection may also give you one or more mailboxes.
Surely if the OP wanted to tie her email address to the contract for her internet connection she wouldn't have started this thread?

There isn't much to choose between the big 3 webmail providers. These days domains are cheap enough to justify buying one which provides several mailboxes. I use UK2 and can use their own webmail which is much cleaner and quicker than Hotmail et al. I prefer webmail as I can access my mailbox from other machines without downloading.