Sounds like you just want something to play around with, to learn about Web servers. Since, based on your message here, you are starting from 0, as far as knowledge goes, you might be better off trying to create a web server on a machine you own, so you can learn how it all fits together and all about security while you are at it.
Just Google 'virtual server lamp' and check out some of the links.
The VPS accounts here at Dreamhost don't feel that different from the shared hosting accounts, you do get the ability to reboot your virtual server, or run your own apache/php/ruby - whatever particulars you'd like to install, and you can create a root user. But, other than that, as far as "Web Design" goes, you can just use a standard account to learn about LAMP web hosting, and you can install almost anything you want your domain, you can even learn how to override DH's standard php set-up.
IMHO, unless you have the web traffic to warrant it, getting a VPS account here is sort of over-doing it for a beginner. It's quite a bit more expensive to run monthly, for one thing.