I am very new to the ocarina and have been practicing from a guide provided with the 12 hole ocarina. Believe me to a newbie this site is a god send.
A simple tune I think I could learn quite quickly would be the tune that plays when you win a fight in Final Fantasy VII, it's up to the creator if they would like to do the bit after the initial tune that plays while you are in the menu right after.
The initial tune stops after 4 seconds of the video linked.