Running your own Linux home server is a fun learning experience about how networks work and using a Raspberry Pi is a cheap and cheerful way to get the job done!
Plus privacy may be important to you. Hosting your own server running your own services gives more control over your data.
Install a stable, well-tested Linux distribution on these wee devices and provide services such as network printing and storage (NAS), perform backups, host web services and much more. Start with a minimal base configuration of Debian or Ubuntu and gain access to tens of thousands of packages ready to install.
Running a Pi server with 24/7 uptime will enjoy more robust performance operating from a hard drive (vs SD card media).
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RPi alternative: Second-hand laptops - retired in favour of more current and powerful machines - can still deliver plenty of oomph for running a personal server. Frugal with power and come equipped with their own built-in UPS (battery)!
Use cryptographic keys to secure access to your new home server.
A terminal multiplexor for creating, detaching, re-attaching work areas.
3. Backup home
Make incremental and automatic backups of a home folder using rsnapshot + cron.
External USB storage + Pi turns any hard drive into a NAS.
Use a DDNS service to automatically update an IP address.
Host web applications using PHP + Nginx + PostgreSQL.
7. RSS reader
Access news feeds over the web with Tiny Tiny RSS news reader.