Image hosting: Piwigo

If you have your own webspace or are planning to get it, then I highly recommend Piwigo for photo management. It's free for you to host on your own, or you can pay for a cloud account managed by Piwigo. The code is open source, the cloud hosted in the EU.

I managed to set up Piwigo with almost zero knowledge of how to do anything with my own website just by following the instructions on their website. It worked perfectly with Filezilla.
There's an app for iOS and Android that's comfortable to use, and at least some photo management programs will have the option to upload to Piwigo (DigiKam for example has it, another FOSS program for Linux. Mac and Windows, also high recommended).

The admin web interface is nice and clean, and on the outward facing site you get a thumbnail gallery with the option to see each photo in various sizes and do some quick edits on it like renaming ect. There is also the option to set up user accounts but I have never done that. You can get a ton of plugins and various themes, apart from the customisation options Piwigo offers right out of the box.

I've been using Piwigo for more than a decade and never had any problems. The only thing I wish is that it would give me the permalinks for the images ready to copy paste but I will live with right clicking.

Screenshots under the cut