Choosing an ocarina to fit the range of a song
The ocarina is fully chromatic, but the restricted range of a single chamber limits the keys which can be practically played. You get an octave with three notes above and—if your ocarina has subholes—one or two below.
This limits you such that, if you play in D on a C ocarina, you actually lose not one but two diatonic notes from the top of the range. You can play up to the high E, but the next notes in the scale—F♯ and G—are out of range.
Practically this means that if you want, or need, to play a song in in a specific key, you need to chose an ocarina in a key that provides the range of notes that you need, and then use cross fingering to obtain the correct scale.
Why not transpose the song to fit?
Transposing the song to fit is fine if you're playing alone, or if your accompanist can also transpose with you, but this isn't always practical. You sometimes have to play in a specific key, such as:
- To fit the range of a vocalist.
- In a pub session (where, in the UK, the keys of G and D are standard).
- Playing with a non-midi backing track.
Just transposing things to fit can leave you playing a song in an uncommon key. Some keys are easier to play than others on a lot of instruments, and practically this means that it can be more difficult to find people to accompany you.
It is also worth noting that playing everything within the same pitch range and key can become fatiguing in a longer performance.
How to choose an ocarina to fit the range of a song
Not every piece will fit within the range of your C ocarina. So how do you deal with this?
If the piece you want to play has only one or two notes out of range, you may be able to alter those notes to fit. But if you want to be able to play in most situations, you'll have to go beyond your C ocarina.
Here's a straightforward example: the Swallowtail Jig in A Dorian. Scanning over it to find the lowest and highest note, reveals that the tune has a range of G to high B. It won't fit at all on a C ocarina in this key.
The solution here is to play it on a G ocarina. As the F♯ is present natively on such an ocarina, no accidentals are required.

Now take a look at the following song, Brighton Camp, which isn't so straightforward. Looking at the key signature, you can see that it is in G. Scanning over the notes, however, will reveal that it has a range of low D to high G—too low for a G ocarina and too high for a C.
As most of the character of this tune is on the high end, you could opt to modify the low notes to fit on a G ocarina. A better solution is to play the tune on an ocarina in D, using a cross fingering for C natural.

Just because a song is in a given key—C, for example—doesn’t mean that it actually fits a single octave starting and ending on the tonic note, i.e. C to C. It's more important to look at the note range than the key when selecting an ocarina. Songs with the key note in the middle of the range aren't uncommon.
Closing notes
What keys of ocarina you need depends on the music you play, and with a bit of practice, it will start to become natural to look at the range of a song, and choose the best key of ocarina to play it.