It is 100% OK to erase the "System Folder", you can verify this is the old system folder by a few things:
1) It actually has Folder in its name.
2) It will have folders such as Control Panels, and Extensions, and the Finder inside of it.
Deleting this folder has nothing to do with OS X, and was transferred for the sake of transferring. Your new iMacs cannot run OS classic and therefore this data is useless.
Things not to do.
1) Do not rename your home folder (Ever!).
2) Do not mess with any files in your computer directory.
3) Do not erase things from the Library folders.
4) If you are trying to delete something and you have to give your password, it probably means you're deleting something you shouldn't. Hit cancel if this occurs.
Otherwise OS X is pretty idiot-proof. But ultimately not 100%.