My feeling is that multi-booting several distros, even with some of them being different versions of the same distro, or even different distros that are very similar, can be a big help in the learning process. That's because being able to go from one to the other and comparing things is a good way to learn about Linux, to see how things are done in different distros. For awhile, I kept multiple versions of Mepis installed so that I could look back and compare things to the current one. I felt that this was a big help for me.
Yes, they can all use the same swap partition and they can access shared data partitions.
My approach, I prefer to use Debian Stable as the distro that boots all the others because that distro will stay in place on my system for a few years, I don't have to concern myself with new releases every six months or whatever. I think that a LTS version from Mint or Ubuntu would serve the same purpose.
Then I have a swap partition and a couple of data partitions that I can access from each distro.
I know that different people have different points of view about all this but multi-booting all linux can be great, it is for me. You don't even need much hard drive space. For a long time I was using one 40 GB drive and one 60 GB drive and booting several distros and I had more than enough space to work with.
I'd suggest using Google to search about things like dual-booting, multi-booting, grub, chain-loading, etc. See how other people have set things up, check out some /boot/grub/menu.lst examples. A lot of the stuff out there discusses dual-booting Linux with Windows but it seems to me that an all-Linux set-up is a lot easier.
I can tell you that the more you do it, the easier it gets, you might run into a few problems but usually nothing you can't work through.
There was an example posted, someone booting 100+ systems, and examining the grub menu there was very helpful to me:http://www.justlinux.com/forum/showthre ... did=143973