Flickr is pretty user-friendly. I'm sure there are others out there. Shutterfly might work, but I've only seen it used for scrapbooking, and I don't know much about it. >.< If it makes you feel any better, I gave up on Photobucket about a year ago. Too many distractions going on there.
The Flickr app is seamless enough with the iPhone camera that it makes uploading pics easy. The one thing I don't like about it, specifically with regard to embedding photos in posts here on BA, is that it's difficult to get down to the *image* URL - meaning that the link you get when you click 'share' in Flickr is not for the .jpg itself, but a link to a Flickr page. On a PC, it's easy enough to get the image file adddress - but on the Flickr mobile app? Not so much! Google's Picassa web albums were pretty good too, for online storage, but I honestly don't know if that's even still a thing! I haven't used it since I stopped uploading photos from a dedicated digital camera in the dark ages (pre-smartphone ).
I use PB all the time. Upload the pic to the Library then click on the pic.Click on the HTTP address next to direct and copy that onto the image button when you post.
http://tinypic.com/ I usually use it for here, there is another site I use for resizing, then upload altered pictures there. I use this site to store place pics and beer pics before uploading here
If you only want it for posing pics on BA imgur is super easy. Upload the photo and select bc or something like that option, copy and paste and boom!
I just recently started using Imgur and have not noticed album capability there. You may have to post pics one at a time.