questionswhat's the best and easiest place to set up an…

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Yahoo owns Flickr.
Google has Picasa.
Imgur is popular on social websites such as Reddit.
I would say Imgur is the easiest based on its popularity on Reddit and how its user base usually follows the path of least resistance. Your mileage may vary.
No fees to my knowledge as these websites just want to get you in the door.
No security to my knowledge because this is the internet and you should always be wary of uploading sensitive information here.

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I'm totally inept with that stuff, and even I managed to figure out tumblr. More or less, anyway.

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I'll second Imgur. It's easy, and free. In addition, I can use it from anywhere (and I have a lot of operating systems, and browsers). I am not a fan of photobucket. Flickr is just sad and pathetic (it used to be my favorite). Picasa is limited in some really weird ways.

Imgur (and thank you, @captainsuperdawg, for walking me through setting it up) is really the best choice.

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Thanks everybody for the information and ideas. I will check them out -- It narrowed it down a lot for me, and eliminate a few.
I'll let you know what I end up with .