I was looking for something similar back in 2011-2012 (without the tagging capabilities) so this answer may not be the most up to date with today's new technologies.

WARNING:

The setup for this requires a lot of technical know-how and you will need to do your own research on what features of Amahi you want and don't want. This is not for someone who feels uncomfortable mucking around with computers.

Amahi works best (in my experience) when you let it be the DHCP server for your home network (or the network your machine is connected to).

---

What you will need:

• A laptop/computer you don't use anymore (the main Hard drive will be formatted!) and that will run 24/7
• Amahi server
• Amahi app for iOS and Android for remote viewing of your data
• A considerable amount of time to set things up right

Setup:

• Follow the instructions on Amahi.org for the full setup.
• Once the OS is installed and Amahi is up and running, you will be able to download the iOS/Android app that will let you remotely access your server files from anywhere. The app didn't have any tagging capabilities for pictures when I used it last (this may be a deal breaker for you).
• From the Amahi server, you will then be able to select which folders you want to share to the app
• Amahi website also has some services/apps that you can install. I don't remember which ones were needed for the web server. You will need to do the research yourself.

---

I did a bit more googling and QNAP seems like something more suitable to your needs. It requires no man hours and technical know-how. I couldn't find any pricing information though.

Good luck!

Feel free to comment here if you need more info. And let me know if you find a better solution because I am looking for one as well :).

P.S. I am just a happy Amahi customer and am not affiliated with them :D