You should actually do both.
• Get an external drive. Make a clone of the old iMac's HD to the new external drive. You want to have a backup once you wipe the iMac for your relative. Keep that backup around just in case.
• Connect the old iMac to the new iMac when Setup Assistant asks if you want to migrate data. Migrate documents and settings. You can also migrate apps, but some might still require a fresh install later on. Anyway, nothing lost in trying. And remember to check all your apps once you're done. If you have old PPC apps you will want to replace them with UBs or Intel versions.
Once that's done wipe the old iMac, IOW zero the disk. Install a fresh OS X. Quit the assistant when it asks for personal data. Then give it to your relative. When he/she boots it, it will launch the setup assistant again and allow him/her to personalize it.