I only have a flickr account, and that's what I use to host my photos - it's very easy to add photos here from there, and I like flickr better than when I had Photobucket.
When you click the arrow to share a photo, you have the option to get the BBcode instead of a link. You can also select the size you want the photo to be when shared:
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loginThe BBcode as copied from flickr will include URL tags to make the image a link as well, but I usually delete those once I've pasted the code into my post or reply, so that it's just a flat image, not an image link.