If you are looking for FREE then there is two options, (1) Blogger.com and (2) Wordpress.com
- Can handle more traffic
- you can use their subdomains, say your-blog.wordpress.com so no need to buy domain
- Limited flexibility
But if are ready to spend few bucks, then I always recommend to go with Wordpress.org (Self hosted Wordpress)
- Need to buy Hosting
- Need to buy Domain
- Can handle limited traffic (Depends on your server configuration)
- More flexibility in terms on design, code and SEO.
Now choice is all yours!