WordPress isn't just for blogging. WordPress powers some of the top websites on the internet and is growing fast. It is now considered to be one of the best and easiest to use Content Management Systems (CMS) there is. See this for a discussion on how to use wordpress for a website here.
If you want to do e-commerce, then you will want to self-host a website on a third-party hosting service such as bluehost, dreamhost, etc., using the software from wordpress.ORG. Figure an overall average monthly cost of around $10 to $25 depending on your requirements.
See here for the general differences: http://en.support.wordpress.com/com-vs-org/ .
If you decide to stay here, yes you can have your own domain name, and wordpress domain registration costs are a real deal ($5 per year for the domain name and $12 to map that domain name to your site here).
If you decide to buy the domain name from a different registrar, you can still map it to your site here.