yes you can setup a web server in your home, but generally speaking, your going to have insufficient badnwidth resources to effictively host your site. Web Space does depend on the size of the hardrive.
If your just putting up some HTML files, you'd be fine with like 10MB of space.
However, I might suggest that you purchase a web hosting package from someone so you don't have to do anythign but upload your site. You can find decent packages for $5/month.