Howto Setup External Drive as a Networked Drive
My suggestion would be to format the drive to the default Mac OS X filesystem, HFS+ journaled. Then share the drive over SMB:


Open System Preferences
Go into Sharing
Check the box beside "File Sharing"
Under "Shared Folders", click the + icon and select the drive you want to share
Click the "Options..." button
Check the box beside "Share files and folders using SMB (Windows)"
Check the box beside the user accounts you want to have access to the drive
Click Done


Once this is done, all you have to do is to configure Samba on your Linux machine to connect to the shared drive.

You could also share over AFP instead and use netatalk on your Linux machine, but I've found that Samba is better supported.