Personally, I choose Google since I know that it will be around for a while. Gmail in the generic form is great, but I use Google Apps so that I can use gmail with my custom domains. Basically, when you send an e-mail to my photography address, I manage that domain through Gmail. This ensures that I have access on my portable devices, and the ability to add more space when needed. If you set up a gmail address, you could also forward all your existing messages to your new address. If you have any questions on the technical stuff, I'd be happy to help.
Gmail itself is great for organizing messages. I have multiple accounts, but one or the best features is the ability to customize your e-mail within each account. For example, I have an address that I use when I sign up for crap online or for online shopping, but it's not my personal e-mail. Let's say it's
[email protected]. I can also add labels within the address like
[email protected] or
[email protected]. The reason that this is important, is that in the future if I start getting spam, and the incoming address is
[email protected], I know which company sold my e-mail. Now I don't use this all the time, and some online forms don't allow this, but at least I can create a label within Gmail to tag all messages coming in from
[email protected] with a distinctive label. Gmail is also integrated into Google Docs, Google Drive, Google+, Google Calendar, etc. So, you get a whole suite of apps when you sign up. Good luck.
Mike.