WordPress is a very popular blogging platform and recently it is seen as the best content management system around. I can tell you that at least for small websites it is from far the best. Depending on what you want to do you ma find it best to use a framework, or to use joomla or other content management system, but when it is about a simple website or a blog the best choice is definitely wordpress.
Due to it's popularity, most hosting providers are advertising their hosting plans as "Wordpress hosting" or "Blog hosting". Well, i dislike their way they try to tell people that their hosting plan is made for wordpress. WordPress has so few requirements that any hosting plan can support it. There is nothing special that makes wordpress work, or that makes wordpress easier to manage or install.
WordPress requires only PHP and MySQL. The wordpress can be installed in few minutes and you don't need any advanced configuration from your hosting.
The wordpress has an auto-update system, but for this system to work the folder permission should allow the php/apache service to change files on the installation directory. Many security experts consider this as an issue that should be disabled, it is true, but when you have a small website it doesn't really matters.
My hosting company, Hostgator, allows apache service to change files, so everything can be done from the administration panel. I strongly recommend it for wordpress website and for any other website that you want to make.
Hosting plans labelled as WordPress hosting are not too bad either, they are cheaper, but be careful at what they offer. Make sure they have all features needed for a good hosting plan. Believe me, you don't want to change hosting plan or company every time you build another website or upgrade.