If you have a Google account, you also get to upload photos that you can then create links for posting. I have only one so far on my account, but find it hilarious:
The only reason I know this works is because I used it in an earlier post after killing my Facebook account and had no way to share personal photos or photos from friends (as in this case). The one issue I had is that I had to put the photo in an album that is open to the public first.
In regards to storage space, this is what is listed in the Google Photos Settings:
I don't know how this compares to Photobucket, but I hope it helps.Upload size for photos and videos uploaded on the web only
High quality (free unlimited storage)
Great visual quality at reduced file size
Original (15 GB storage left)
Full resolution that counts against your quota
Also, in regards to Dropbox, which I pay a pretty good penny for, I couldn't get a photo or video to embed on this post.