Free blogs on Blogger or Wordpress.com are fine, but if you are serious about it at all and plan on putting in a lot of effort, you should definitely buy your own domain name and hosting.
It's pretty cheap, Wordpress is great and free, and you own your site. If you make a blog hosted through Blogger, they technically own your site and your options are very limited. I think people also tend to respect independently hosted blogs more because it shows a certain level of commitment and professionalism.
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