What type of ocarina should I learn?

Now that you are aware of the types of ocarinas that exist, you may be wandering 'What type of ocarina should I learn?'

The different types of ocarina can be broadly split into two categories:

Melody ocarinas, ocarinas designed for playing monophonic melodies.
Harmony ocarinas, ocarinas designed for solo harmony performance.

Functionally these can be considered different instruments, having notable differences in design, limitations, and musical function. Thus they have been addressed separately.

Melody ocarinas

The following types of ocarinas are the most applicable to playing melodies:

Transverse ocarinas, including multichambers
Inline ocarinas
Pendant ocarinas

Of these, I think that the best type of ocarina to learn for playing melodies is a transverse ocarina, as:

The transverse ocarina has been refined over many years. They have been made by numerous makers over more than 100 years, specifically for serious playing.
Transverse ocarinas can be tuned extremely accurately. They have more balanced volume (loudness) between adjaced notes in comparison to pendant ocarinas, as there are no irregular changes in blowing pressure. Also it allows you to focus on playing music instead of compensating for tuning errors.
Inline ocarinas have less refined ergonomics. Playing well requires supporting the instrument when leaping between notes at the extremes of the instrument's range, and inline ocarinas are not as developed in this regard.
Single and multichamber transverses use the same fingering system. You can progress to a multichamber ocarina as your skill develops without needing to completely start over.
Transverse ocarinas have similar fingerings to other instruments. If you already play, or are interested in learning other wind instruments it will make your job easier.

One remaining question that you may have is if it is better to learn to play a single chamber, or multichamber transverse ocarina. If you are new to music, a single chamber will be simpler as they have fewer notes. For more experienced musicians a multichamber may be preferable.

Inline ocarinas may be preferable is if you have RSI, arthritis or other disabilities. If it allows you to play when you otherwise could not, that's awesome.

Harmony ocarinas

Harmony ocarinas and Huaccas have interesting potential in musical performance given that they allow you to play in harmony with yourself an improvise. They are worth learning for an enterprising player or composer, and do offer interesting musical possibilities.

However if you are inspired to learn to play harmony ocarinas you'll need to look elsewhere as I won't be mentioning them again on this website for a number of reasons:

Firstly, I don't play harmony ocarinas, and thus do not have the experience required to offer advice on playing them.
Secondly, harmony ocarinas are not standardised at all, which makes it extremely difficult to offer useful advice. It is impossible to know what, if any, kind of harmony ocarina you would be able to obtain.

Nancy Rumble is a well known serious player of harmony ocarinas, and studying her playing would be very valuable. Also, look for makers of harmony ocarinas and read any documentation they have provided.

Closing

For the remainder of this website the focus will be on teaching the design and mechanics of the transverse ocarina, as they are the most standardised and available as noted above. Much of this information is applicable to other kinds of ocarina / vessel flute, and can be adapted with little effort.

But, whatever type of ocarina you choose to learn, I'd advise choosing one type and sticking with it.

Playing any instrument well requires not just a conscious understanding of mechanics like breath pressure and fingering system, but deep subconscious knowledge commonly called 'muscle memory'. Developing that subconscious knowledge is done through the repetitive practice over months, if not years, and once done cannot be easily changed.

Consistency in instrument design is important as It allows you to continually build on and refine technique, even if you play multiple ocarinas, or move to a better quality one.