Server options for late 2006 macbook
You are correct Mountain Lion will probably not run on it.  Also you need server software for it to be recognized as a time machine location.   Not sure if that was available in previous versions though.  OSX server is powerful,  but for simple use it is probably an overkill.  I have spent to many hours tinkering with mine while just using it for the uses that you state.

If you can get hold of an older version of OSX server and you are willing to tinker.. you could do all of that though