I'm a control freak when it comes to my own sites, so I don't trust anyone to host them except myself.
As to a host, however, the specifics of what you plan on doing might affect what host to look for. GoDaddy is a very financially stable company which means something... Aquisitions are extremely common in the web-hosting world. I've had some GREAT webhosts in the beginning be purchased by asshats and end up screwed. That happened with Doorhost, i vehemently recommend avoiding them.
That said, GoDaddy is a bit high on price though it's still really reasonable, at around $6 for their basic hosting. This is per site per domain per month, so if you plan on extending out and adding domains within the next year, it MIGHT make sense to factor that into the host you have now, since moving is a pain in the butt especially if you get a host that isn't fond of you leaving.
Also, what you're planning on doing as far as content is important. You mentioned the idea of a Google blog... If that's all you're doing, it is possible to point your domain name to the blog, so that yourdomain.com points to your content, no hosting needed. If you'd rather install your own blog (say, to add customized themes, plugins and ads) then you're going to need hosting.
And finally, please, please, please, please, please... if one thing in this thread changes your worldview, it's this... Backup your site. Yourself.
http://www.monochromementality.com/...Site-Broken-Articles-And-Learning-Python.html
I had a server with redundant RAID which creates a statistical chance in hell of something being totally destroyed. I also kept snapshots of my server with my host and updated the backup I had on my home fileserver but unfortunately I'd neglected it for a few months.
When one hard drive failed, the company I'm with rushed in to replace the bad drive, which wasn't interrupting my service since the other was functional - a common occurance. As the one drive was restoring it's mirrored buddy, it too failed, which is a statistical blip in and of itself. And I learned that the snapshots were stored on the same server... So my site was entirely gone and I was left restoring from a combination of my 3 month old backup (can you imagine loosing 3 months of HBT's posts?) and Google Cache.
So back. Your. Stuff. Up.