I have no idea which is best. Frankly it seems like there are too many choices.
Probably MessagePack, since it is JSON-like and I've actually heard of it.
I'm not sure what Avro is doing, but as a rule schema enables you to have less overhead, rather than more. The main advantage of MessagePack over schema-based formats is that it's dead-simple and mostly compatible with JSON. Schema-based formats usually need either a code generator or maintaining an annotated version of your data classes and making sure they match the schema.
(Of course, with JSON or MessagePack you might still end up using a serialization library and something like JSON Schema).
The elegant thing about MIME is it allows multiple encodings and cross-references, so you can have your HTML and the images displayed in the HTML both optimally encoded in the same document, which was handy back in the time when HTML emails were taking off and marketing insisted that the fancy image signature they designed had to show every time, even when the person was reading the email offline…
Of course back then we had to encode the image in base64 anyway because of non-8-bit-clean email servers. But I digress and will go back to my rocking chair.
There seems to be a common trend of people writing "JSON APIs" thinking that every other part of HTTP is off-limits.