Constant force springs would be a good method to counter-balance an elevator. They're pretty simple to use, you could have one for each stage. I believe 846 and 973 used them in 2011 on their elevators with success, i'm sure many other teams used them as well just none come to mind. Hope this helps.
As far as how much to counter-balance I would not completely counter-balance it, just enough to prevent back-drive. This is just what I would do if building an elevator though, I only have experience designing an elevator, not building or using one for an FRC application.