I'd like to include an image in a posting and after I select the image icon I get a dialog box saying "Please enter the remote URL of the image you with to insert" Followed by a http://

I take it that you can't attach or insert an image directly into a posting?
If not, then where would be a good (i.e. free) site to post my image and then link with an URL to it?[/i]

http://imgur.com/

http://imageshack.us/

I do not trust any image-uploading website (eg: imgur) that changes the image one uploads, whether it be re-converting, lowering the quality, or whatever.

(Note: I also do not trust any image-hosting website to keep one's image online around forever.)