I would suggest Gmail. It has about the best features and customization that I have seen and its free. It uses IMAP which will sync your mail, contacts, calendar, etc on all your devices. So if you use Outlook, a smart phone, and the web application, they will all look the same (if you read an email on your phone, it will show as read on your Outlook and web browser). Gmail also has a boat load of storage. I haven't deleted any email in the 8 years I have been using it and still am only at 15% total storage use.

Also, if you are worried about those contacts that you have already. You can forward your yahoo mail to Gmail, and you can also setup a "send as" account in Gmail to send mail from your Yahoo email address through Gmail. I use this so that I don't have to login to multiple accounts and still send/receive email from more than one account. Importing contacts and mail from Yahoo is pretty easy too.

Just my 2 cents...