The first thing I need to say is that I have nothing against Blogger, Webbly or any of the other blog publishing services. There are pros and cons of using a blog publishing service, but I feel you are better off hosting your blog independently and using a good quality CMS like WordPress to allow you to easily post content to your website.
The biggest reason for owning your own domain is that you stay in complete control. If you use a blog publishing service, the firm that runs the service is in control.
It is possible for them to take your site down at any time. In theory, if you stick to the rules your site will not be taken down, but it happens. Understanding the rules, remembering them and sticking to them is not easy. Add in the fact that the rules can change at any time and you can see that following the rules to the letter can be quite tricky.
If you buy your own domain and host it independently, you are in control, at all times.
In addition, many blog publishers put restrictions on how you can monetise your blogs. They may not let you put affiliate links on your website or ad banners. Adding a shop to your site is also usually not possible. If you have your own website, you decide if and how you make money with your website.
Endless site design options
WordPress is a fantastic content management system. There are endless themes, plugins and widgets to choose from. This makes it easy to make your site look the way you want and to add additional functionality to help your readers to navigate and use your website.
WordPress is available in 150 languages. Most blog publishing services are only available in a few languages.
A last word
If you do choose to go with WordPress I strongly recommend that, you find a company that offers WordPress hosting. Doing so makes it much easier to get the CMS up, running on your site, and keep it up to date. It is also designed to speed up your site. Given the fact, the speed at which your site loads is an important ranking factor how fast your website loads is important.
As I said at the start how you set up and run your website is very much up to you. There are pros and cons to both approaches, but I prefer to stay in total control of my website, which is why I have gone down the self-hosted route and recommend this approach to others.