Dreamhost uses Debian on their servers, but I don't think using the same distro is going to change anything. It's probably best to use the one you're most familiar with, since you're the one that has to keep it up-and-running at home.
I never tried to duplicate their environment, but I'd guess that you might be able to pick up how some things are setup by running a PHP script with phpinfo() in it.
I doubt Dreamhost would want to share any info beyond what we already have access to--especially panel code and anything else below the home directory.
The only thing I do on my computer (using Windows, no less), is setup Apache, PHP & MySQL. Then, I make a folder for each website and use the same directory structure that I have here. If my account & .snapshot backup happen to vanish, I have it here and could upload it again without having to modify anything.
I think the main thing you really need to duplicate on your computer would be coding habits. Obviously, if you need root access to get something to work at home, it won't be happening at DH. If I'm playing with something at home and have doubts about it working here, I just SSH in and throw up a quick test script to check for problems.
As far as PHP goes, remember that it runs as CGI under your user here, so you might run into some differences if you're running at as an Apache module at home. I don't do anything with Perl, Ruby, Python, etc... so I don't know what you'd run into there.
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