You don't have to partition the hard drive to use it as you've described, although Disk Utility does make it easy to create the partitions. Partitions are a logical construct that makes the one physical external hard drive look and behave to the Mac as several different hard drives. The ideal time to create partitions is right after putting the drive in use, since creating partitions afterwards requires reformatting the disk, losing whatever was copied onto it in the meantime. The advantage of partitioning is that you can have one partition set as a clone image of a known-good state of the computer, and leave that known-good clone alone just in case you ever apply a software update that fails and hoses the internal hard drive. The rest of the drive can be used in one or more partitions for an incremental daily backup of key data, a partition for data in active use (music and images), a partition for archived stuff --- whatever uses occur to you. But as you've noted, if you want to keep it simple, you can just use the external as one huge storage location. The only thing that's really essential is to have a backup of anything that irreplaceable, by copying those files to the external drive.
It's prudent to keep about 5 GB free space on the internal hard drive, for such things as Unix cache files, temporary DVD burn images, and if ever needed, space for an
Archive and Install.You can easily copy user data from the internal to the external drive by drag copying in the Finder. Music, photo, and movies files are a good place to start. See these Knowledge Base links:
iTunes: Moving your iTunes Music folder
iPhoto: How to move the iPhoto Library Folder