Though Bottom often steals the show in performance, Puck is usually considered the most important character in A Midsummer Night’s...

If you are considering a Comedy structurally, then neither
Puck nor Bottom is the protagonist.  Both are characters whose actions (Puck) contribute
to the complications of the main plot or whose actions (Bottom) comprise a subplot that
comments on the characters/events of the main plot.  Since neither's actions are
actually the driving force of the main plot, neither can be considered the protagonist. 
So, who then, is the protagonist?

Classically, a comedy
must end in at least one marriage, and it is the central character(s), the
protagonist(s) who go(es) through the main trials and tribulations of the play, only to
have all ironed smoothly out for the "happy" ending in
marriage.

One such charcter is Hermia.  She begins the play
in a dilemma (similar to a dilemma Juliet faces in Romeo and
Juliet).  She wants to marry for love to Lysander, but her father wants her
to marry Demetrius.  She is given an order to marry Demetrius or else suffer the
consequences -- be killed (!!) or join a nunnery.  She decides to flee to the forest
with Lysander.

There is also a case to be made for Helena
as a protagonist, since she is in love with Demetrius at the beginning of the play, and
creates a plan to alert him to Lysander and Hermia's scheme and  then follow him, hoping
to win back his love.

A great deal of the mischief and
mix-up in the play revolves around the young lovers' story lines.  As a group, they
could be considered the protagonists, or you could make a case, as I have done above,
for one of them.  And, as is traditional in Shakespeare's comedies, there is a subplot
invoving low-born characters, the clowns, who are in the play to entertain the audience
in the very ways you describe.  They are often the ones who "steal the show."  But this
does not make them the protagonists of the story.