Blogger.com is where you want to be.
You can upload any of your own videos to Youtube, then embed them into your blog as you normally would.
Same deal for pictures, but you could probably setup a Flickr or Picasa account for those. I believe blogger does do some image hosting, just not full on galleries. So it's good for 4-5 pictures per post, but beyond that you'll want one of the two services I mentioned.
If you really want full control over things, you can setup a full site that handles everything, but it's quite a lot of work to get functioning. The Wordpress blog software is the best in class at that though (not to be confused with the Wordpress hosted service).
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