What service is good for posting an image that can then be linked to on this forum?
I recommend imgur over any of the others for multiple reasons.
Imgur does not require signing up, however if you do you can manage your images later.
(honestly, is this your biggest hangup?)
Here's a secret (?) Dropbox tip. Dropbox gives you a link for the file that looks like:
Change it to the following to get a direct link: