I managed to upload to photobucket, but how do I tell photobucket to produce/disclose a unique URL and how do I tell the board about this URL?
Click File when you are on the page viewing your picture. Highlight Send, which is near the bottom of the window that opens. That in turn will allow you to do various things with the url that is required. Choose Link by email. You need not send it, just copy the link, which would then be posted with your comments.
Your other option is to host your pictures on the Chaski board. As you mentioned, there are size limitations, but they apply regardless of where your pictures are hosted. The only exception to that is if the pictures do not execute automatically. I don't care how large they are as long as they don't spread text on the typical monitor, which operates @ 1024 x 768.
Hope this helps. I use only the Chaski board to host my pictures, so I'm not well acquainted with the other options.