can I run my own website from my computer?
I really wouldn't host a website from my own computer - too many security and bandwidth issues, you really need to look into web hosting - your ISP probably provides you with some web space to host a home page already.
As already said, Blitz is a programming langauge so it is not useful at all for building web sites, use something like Macromedia's DreamWeaver (I wouldn't use Word or FrontPage as they create very Microsoft specific web pages) or if you want to get into the HTML then find a good book, there are plenty around.