I don't use Fedora, I'm on Ubuntu. I always just run the installer as my day-to-day user and install in a subdirectory of my user home. That works well for me and this also the kind of setup that we test before each release of STS and GGTS.
So generally, unless you really have a very good reason to want to share the IDE installation with multiple users (e.g. in some corporate setting where users only allowed to use centrally installed and authorized software) it is probably best to just install the IDE as your day-to-day user in that user's home dir.
I wouldn't advise moving the installation around and trying to fix file permissions, ownership etc. Theoretically that is possible, but I think it is probably easier and less effort to just reinstall.
Kris De Volder -- SpringSource