It's really important once you get online to get website hosting and have your own self-hosted blog or website. It will give you more control over your own content. I, personally, really love blogger so I am still over here blogging on several blogs while I also have hosted sites. I know I should probably give Blogger up, but, I just can't seem to completely walk away. Silly, I know.
I know some people buy their domains and still use Blogger as their CMS. I don't really know, though, if that really puts you in the driver seat or not. I suppose if you are making regular backups, you would still be safe. But owning the whole site, kit and caboodle, is the best way to go.
For my hosted sites, I actually have three different hosts. My favorite website host, though, is HostGator. You can read all about them, along with some reviews, at that link.
It can be so hard when you are going into something new, so it really helps to have a ratings and review site, where you can get stats on the different companies and impressions from real people on their experiences.