Like others, I think that a Wordpress blog with your own domain is great. If you are still new to blogging and don't necessarily want to use your own domain, I recommend Blogger. I've used both Blogger and Wordpress, and I just prefer it's overall feel.
My first blog was hosted on blogger, mostly because I didn't have a paypal account yet and couldn't get hosting. In the long run, it is better to opt for wordpress as you can make a backup of your files. I don't think it's possible to do that in blogger, am I right?