:cloud: ownCloud web server core (Files, DAV, etc.) (by owncloud)
If you'd use something like your own http://owncloud.org/ you could have a pretty much google alternative for everything in once place. (Mail, Calendar, Documents, Photos, etc)
Runbox 7 web app
I wouldn't call this the "best" option. "Best" is tied to a specific case, and OP's case isn't clear to me. I've self-hosted my mail for ~5 years, and I moved on to runbox.com now. Not expensive, cheaply hosted with green energy in Norway and their web UI is free software.
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Could an old ideapad be a mini file hosting server?
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