Thoughts: The dilemma of device-bound data

Recently the power supply of my main PC (that is, a regular PC with an old dual-core Intel) just died without a sign of trouble beforehand.

Since I still don't have a NAS and my data on this PC is spread over several hard disks inside I didn't have access to this data while my PC was out of order.
Especially using (and looking up) some E-Mails I really needed really was annoying since I had to use my external backup drive (1TB USB 3.0) on an laptop to get to those files. Being cautious while loading the backed up Thunderbird profile on that latop from my backup drive is necessary because I still do have some good old POP3-style accounts. Now, downloading data from these accounts while running a (temporary) backup profile would be very bad because all this data then would be lost or at least difficult to merge with my "real" profile later.

As more and more people move their data into clouds, on private servers or NASes here's my personal list of items I really should think about becoming an ubiquity:

- Old-style POP3 accounts; only use fat clients (e.g. Thunderbird) for IMAP
- Let retrieve IMAP accounts those old POP3 accounts (hosted by third parties)
- Personal data like pictures, documents, encrypted stuff
- Business data

As I already use a Dropbox alternative for some daily-use and small data I really would like to have a self-hosted cloud solution where I'm finally not bound to any device anymore. Even these two days where I wasn't able to use my main PC I recognized pretty fast - regardless of the backup I had - how much (important) data still is bound to it.

What do you think? Suggestions? How to you manage your daily data-life with multiple devices?