Our avatar should look like a normal old man, maybe hunched over with a cane and long beard. Big bushy eyebrows, the whole deal. We don't need extra flamethrowers because we're a god and can just do the same thing without even needing to move an arm. And talking to a old smiling grandpa would be a hell of a lot less terrifying than trying to talk with a giant 12 armed golem that would make Lovecraft shit his pants.
It could also serve as a nice disguise, if the other gods don't have some means of sensing our soul walking in their territory. A old hermit wandering into town isn't a big deal, until he goes nuclear, and by then it's too late.
As for limiting mobility, presumably we wouldn't even need to go wholesale into him. Just a fraction of our consciousness could reasonably mimic a human, hell computers nowadays can seem to be sentient easy, and we're GOD.
Here's a good question.
WHY?
Seriously, what makes you think that a god would be unable to sense a god hiding in a mortal frame? And what could we gain through such deception?
Well it's fairly obvious that gods don't notice everything going on in their area at once. Like mortals, we can only "see" one area, though our followers can call out to us.
So if we had on that disguise, unless he was looking for us or happened to pass by too close we'd be fairly invisible. His followers wouldn't notice, I bet. the theoretical god we're scouting would have to happen to be passing by where we are, unless we're so huge as to have a great gravitational effect on whatever weave the mana comes from and they sense that. Which is a possibilty.
As for what we would gain, probably little. But we wouldn't gain anything from a gaint abominable robot body either. If we make an avatar, let's be subtle. Chaos and fire don't have to be raging all the time, and life is good at camoflauge.