You can do most (pehaps all?) of the above by unattended network install of Fedora, and (altought I'm not that familiar with other distributions) you should be able do the same at least with any of the larger/most popular ones.
What distribution do you want to install? (No, a "homebrew system built by me, myself and I" won't ever come close to anything that merits installation on dozens of machines; there are literally many thousands of people, with a sizeable number employed full time, behind any of the more popular distributions, and a few hundred behind the smaller ones. Only distributions that are not much more than a spin of a major one can get away with less manpower.) The answer to that will narrow down the options significantly. Look at what Amazon and other "cloud" vendors provide for their virtual machines, you might be able to swizzle much of that for your own use. Check what the webhosting/-housing outfits use, see if you can pilfer something there.
Make sure that whatever you use has a proven track record, and isn't likely to dissapear from sight anytime soon. Make sure the licenses involved are clear (getting into legal hot waters isn't fun) and to your liking.