AT&T email and using Live Mail

Most email clients have an option to leave email on the server (or possibly worded not to delete email on the server).  But I would suggest you just use email clients on both your computer and your phone set up to use IMAP.  Then both clients can access the email as if you were using only one (i.e., if you read an email on one you don't see it as unread email on the other).  Both are kept in sync by keeping the original stuff on the server, which in this case would be the att/yahoo email server and thus there would also be in matching mailboxes on the webmail which you can see there too.

I suspect you already are doing this since most phone email clients default to using IMAP and I suspect that Live Mail probably does this also.  So going back to what I originally said make sure these clients don't specify deleting mail from the server (or specify keeping mail on the server depending on how they word the setting).