I teach the third required intro course in a CS department. One of my homework assignments asks students to speed up code they have written for a previous assignment. Fact
Subversion on Windows can be as simple as setting up TortoiseSVN. There is a bit of a learning curve for using it (especially if you've never used a version control before), but you might help that by dedicating half a lesson to it and providing some powerpoint slides for them to download.
As for centralization - I've heard of websites that offer free SVN project hosting. A quick Google search turned up this page, but there are certainly more.