Here is the deal...most isp do not let you run a web server...however they do leaves ports open which you can use to host a site...Most isp will leave port 8081 or 8082 open which i use for my web server....
so a user would enter
http://mysite:8081
or if you use your routers ip address it would be
http://168.151.1.1:8081/mysite
Dreamweaver is ehhh. Not sure how much it runs but its good for non dynamic web sites.
For dynamic sites u will need something more such as visual studios or an open source architecture.
As far as the web server...you really don't need to dedicate a whole computer if your not expecting to get alot of traffic.
If your just not using asp or asp.net then you can use apache which is free. Google apache and download it etc. (IIS is easier to use though)
Another option besides Apache is Microsoft IIS it actually comes with Windows as long as you have the professional edition.
If you have the pro version then control panel, add remove programs , add remove windows components, then install internet information servvices....
the gui to configure it will be in your administrator tools then internet information services