Unless privacy is a concern (you were on Google photos so far) you might try Dropbox, Amazon, Flickr, One Drive etc. As for self-hosted, think real hard whether you want to be dealing with everything that comes with it.
If I had such a need and privacy was not an issue I would use Dropbox (I already use Dropbox a lot, easy to share, excellent download speeds, and I don't have a huge photo library).
No matter what you do, stay away from iCloud. By God, they have made it so bad that it feels like a criminal offence.
I tell you what I was trying to do just now. Literally minutes ago.
I have photos in "Library" (i.e. the first screen that loads) and I didn't want that. I wanted them in different albums and just stay there. So I added them to different albums. There's no way to "move". They will still show there.
Now you can hide them from "Library" and they will vanish from the Library. Awesome, right? Nope! They vanished from those other albums you had added them into as well. Now those photos are in a special library called "Hidden". Yes, all those photos!
Okay fine. Now you want them back in those albums. So you go to Hidden and select some photos to be added into an album. Everything happens fine it just that the photos still don't show anywhere but only in Hidden. So I guess you will have to first unhide those photos and get them all in Library and then add them all to albums.
And all I wanted was to keep the photos that processed (i.e. moved to diff albums) and the ones not processed separately.
Now I don't even want to start on how my friends exclaim "What kind of service is this? Which company? God such a pathetic download speed!". Those friends are from all over the globe.
If I had such a need and privacy was not an issue I would use Dropbox (I already use Dropbox a lot, easy to share, excellent download speeds, and I don't have a huge photo library).
No matter what you do, stay away from iCloud. By God, they have made it so bad that it feels like a criminal offence.