To transfer files, NFS is the choice
add lines to your /etc/exports file that specify the directories you want to share (This will make them world wide visible) For more info see man exports.
Then restart/start your nfs-server. (Don't know how this is done on RH.
You will then be able to mount the directories with the command
#mount -t nfs server:share /mount/point
where share needs to be the fully qualified path on the host machine. That is if you shared /share/music
you will have to mount like this:
#mount -t nfs server:share/music /mount/point
You will probably have to create one identical user on both machines, so you won't get into file permission issues. For the time of transferring its probably a good idea to make the files world-readable.