The second seems correct, but the others arn’t.

If you talk about yourself you should use “Voilà que je me mets à” anyway.

But then again i have never heard anyone here in a french speaking country using any of the three.

The third form is incorrect. Here mettre need to be used with a pronominal form.

The first form is correct although rarer than voilà que je me mets, especially here at the first person. Other persons are more common:

Me voilà qui me mets…
Te voilà qui te mets…
Le voilà qui se met…
Les voilà qui se mettent…

The second form is even rarer and less idiomatic but still correct:

Me voilà me mettant…
Te voilà te mettant…
Le voilà se mettant…
…

There is also the colloquial form:

Voilà pas que je me mets…

and this even more colloquial (but ageing in France) one:

Voilà-t-y pas que je me mets…