You could just start with "plain" Ubuntu, Linuxmint, or Debian, etc., and just add educational packages. You could also just run a specialized Linux distribution...
Besides trying to find a distribution with the features I like already in it or a distribution starting from scratch where I could contribute and add features I need, I have been investigating the possibility of customizing a popular distribution with a lot of available packages. My first choice would have been Slackware because I felt comfortable with the package manager. However, I am unable to get the latest versions to work on my main desktop computer or my laptop. I've seen several recommendations for using Debian with the netinst (or Anti-X based on Debian minimal install disk) and then customizing the system to get it the way you want. Debian also provides a great deal of choices as far as how you set up your system such as different Linux kernels (including Liquorix), alternative userland tools (such as Busybox) and alternative init systems (such as file-rc and runit). Plus, unlike Ubuntu, Debian provides a stable branch that I don't have to worry about upgrading for a few years. I've heard great things about Linux Mint especially from my local Linux Users Group, but am unable to get the install DVD to work with my desktop machine. Out of about a dozen different distributions I've tried on my main desktop machine, only two have booted successfully. (I have a lot of unusual hardware in my desktop machine.) If I want an operating system that works on my older laptop as well as my newer systems, that narrows down distribution choices even more.
Despite the fact that I dislike Debian's package manager from a package creation standpoint, it is very usable from an end user perspective. I put together various information and some scripts I've been working on in order to sneakernet Debian packages from a system with a fast Internet connection to a system with slow or no Internet connections. That way, I can update one system and use it to sneakernet and update the others. In case anyone's interested, the information is at http://www.distasis.com/cpp/snet.htm
One of the things I'm looking into is running a minimal stable Debian base system and adding my own build/package management tools and my own up-to-date packages (possibly in /usr/local or a home directory). I'm also trying to find lightweight educational software that runs well on older as well as newer systems. I prefer building applications from source if possible and don't have any issues with patching to make applications more stable or to add missing features I personally need. If I find any useful applications, I try to add the information to the Schoolforge web site software list. As mentioned, I'd really like to find a distribution or project where I can share some of the things I'm working on (such as patches to older software to deal with memory issues/bugs/library updates, utilities I'm creating, etc.), but have had no real luck finding an outlet to share code so far. (I do send fixes first to the original project maintainer if there still is one or if the project is willing to accept patches.) Always interested in new recommendations for programs to try out and look forward to seeing what others post to this list or the Schoolforge web site list.