These are the gentlest tabs in the library for a 12-hole ocarina, easiest first. Each one is rated from its notes alone, on four things: how many notes it has, how far its lowest note is from its highest, how many sharps and flats it uses, and how often it jumps by more than a fifth.
Those four are what make a melody hard on a 12-hole ocarina. A wide range takes in the thumb holes and subholes and needs steadier breath at the top and bottom. Sharps and flats use forked fingerings or half-covered holes. A big jump moves several fingers at once, and a long song is simply more to remember.
First songs
Short tunes within about an octave, with no sharps or flats and no big jumps.
Prelude of Light by Koji Kondo. Easy: 12 notes, A4 to D5, no sharps or flats.
Requiem of Spirit by Koji Kondo. Easy: 12 notes, D4 to A4, no sharps or flats.
Zelda's Lullaby by Koji Kondo. Easy: 14 notes, G4 to D5, no sharps or flats.
Hot Cross Buns. Easy: 17 notes, G4 to B4, no sharps or flats.
Jesus Loves Me by William B. Bradbury. Easy: 49 notes, F4 to F5, no sharps or flats.
Camptown Races by Stephen Foster. Easy: 50 notes, C4 to C5, no sharps or flats.
Misty Mountains (The Hobbit) by Plan 9 (David Donaldson, David Long, Stephen Roche, Janet Roddick). Easy: 57 notes, A3 to A4, no sharps or flats.
Arirang. Easy: 61 notes, D4 to D5, no sharps or flats.
Skye Boat Song. Easy: 64 notes, C4 to C5, no sharps or flats.
Ballad of the Wind Fish by Kazumi Totaka, Minako Hamano. Easy: 20 notes, E4 to F5, no sharps or flats.
How to learn a new tab
Learn the notes before the rhythm. Go through the fingering charts slowly, one phrase at a time (each line of a tab is a phrase), until your fingers find the holes without looking.
Use the playback on each tab page to hear how a phrase should go, then play it back. When a phrase is easy, join it to the next one.
When these feel comfortable, try the Ocarina of Time songs. They use only five notes, but they move around more than a nursery tune does.