Best bet IMO is to have somebody inexpensively host it for you under your own domain name.
Some, like Godaddy, will give you one free mailbox if you register the domain through them. Basic POP3 e-mail host plans are also pretty cheap no matter who you go through. I'd suggest paying the small premium for an IMAP account. That way your folders will automatically be in sync among your devices if you still want to use an e-mail client. No need to futz with PSD and other message stores if you get a new machine either. And you're also backed up because your messages remain on the IMAP server.
If you already have a registered domain I'd strongly suggest springing for some small (5-20 mailbox) hosting plan. Prices are low, and there's some real bargains if you shop around.
If you're an Outlook fan who needs the full functionality, go with Microsoft's Exchange Online service. It runs about $5/mo per user with no contract. With that you get the full capabilities of Outlook, like shared calendars and contacts, invites, etc. It's a very good deal if you need all that. And you can pay it month to month so it's very affordable.