Choosing a Hosting Service
There are two powerhouses in the free blog market: Blogger and Wordpress. In the last year, Tumblr has also muscled into this market. You get nay-sayers on both sides of the isle, but let me give you my impressions of the free sites, then discuss briefly buying a domain.
Blogger
Blogger is operated by Google and is considered the easiest of the free sites to use. It provides a wide array of layout options. But being the easiest to use, many people consider it a poor hosting site for professionals. Kinda like a bike with training wheels. 1 GB (gigabyte) of image storage space is provided.
WordpressThe main difference, as I understand it, is the code. Wordpress is considered more 'designer friendly,' meaning if you know web design, it's easier to code your own page. Since I haven't written my own html code for almost ten years, I don't know if that's true or not, but it seems to be the general opinion.
Wordpress comes in two flavors: Wordpress.com & Wordpress.org. The .com version is the free side of Wordpress and inserts ads into your blog. The .org side hosts Wordpress' pay to play features. 3 GB (gigabyte) of image storage space is provided.
Really, with any of the free sites, you'll get about the same service.
I personally went with Blogger because I wanted something simple, and while it has been fairly easy to use, I've still had to spend a LOT of time reading tutorials and trying new things on my blog. But I personally want it to look professional, so I try to push my layout. I've never ran into something that made me regret choosing Blogger.
Content Ownership
The main disadvantage with blogging on a free site is content ownership. For most free sites, you're going to have to accept the hosting companies Terms of Service. Take, for example, this little clause in the Google terms of service for Blogger:
When you upload or otherwise submit content to our Services, you give Google (and those we work with) a worldwide license to use, host, store, reproduce, modify, create derivative works (such as those resulting from translations, adaptations or other changes we make so that your content works better with our Services), communicate, publish, publicly perform, publicly display and distribute such content. The rights you grant in this license are for the limited purpose of operating, promoting, and improving our Services, and to develop new ones.What's that mean? Google can use anything you put on your blog to operate, promote, and improve their Services, and to develop new ones. So if you create a new feature for your blog or hire a programmer to design something for your site, Google can take it.
Buying Hosting
Alternatively to free sites, you can buy a domain name and hosting space. Prices are cheap and when you do, the web page and everything in it is yours. But unless you know web design, you'll have to purchase a layout and figure out how to upload your content. There is a little bit of a learning curve, but html is fairly easy to pick up. It just requires the time to learn the language.
My advice? Start off simple with one of the free sites. Then, when you're ready to invest in something more serious, make the change.