I highly recommend you go with http://vox.com although Blogger, Typepad, Wordpress and LiveJournal are all also well-knowns that work well.
Vox is FREE, seems fun and energetic and easy to use and has a lot of options.
You could also try creating your blog at http://weebly.com and that would let you easily add YouTube videos, Flickr photos and such to your blog.
Feel free to contact me if you need more info.
http://squarespace.com is also NICE in design, but NOT free, which I think is the key if you are starting from the basics and want to see if it works for you.
I'm on http://tribe.net, which is great if you are looking to blog AND have a social network and a place to show photos, videos, etc. for free - I love it. Check mine out at http://people.tribe.net/ecrivaine32
Glad to help!