Buy David Power's book on working with php, mysql and dreamweaver. There is a very good walk through on how to get up and running with the three together. I also think there is a series of videos on the WebAssist site that effectively do the same, so have a look there first.
Once you've got the setup right, you'll need a gui like MySQL administrator or a better one is HeidiSQL (both free). The gui's help you to build a database without the need to know MySQL code.
In most cases you take a template you have designed and run the WebAssist extentions in DW... hey presto, you've built a website that is pulling data from a database in less than an hour without needing to know any php/asp/cf code. You're then able to alter then design if you wish.
There are funny quirks when applying the extentions, but as long as you follow the tutorial videos on the site, you'll be fine.
Overall the WebAssist software has been well worth the purchase for me.
As for building, you build locally and test locally, then upload your site to a live host. Running Apache, PHP and MySQL really doesn't take up that much computer resource. I have a midrange laptop that is four years old (40 gig disk, 2 gig of ram, 1.4 ghz chip) and that really doesn't even break a sweat when building websites, after all, you are working with small files that need to be downloaded/viewed over the internet.