In terms of Godzilla's look, then I'd say bring back the MireGoji suit (Favouritism?
Watakushi?
), give him the silver dorsals of
GxMG/
Tokyo SOS and bring back the golden-hued eyes and double rows of teeth from the Heisei series. But, mrbluehair, I do like your idea of bringing back the 'ionised air' effect from just before Godzilla cuts loose with the heat beam in
GMK.
As for what I would like to see in the next movie - well, it would be nice if there could be a rampage like
Gamera 3's Shibuya battle between Gamera and the Gyaos, something where we could see some fall-out of Godzilla's attacks rather than an evacuated city. Of course, that would be a bit tricky to still have humans getting caught in the crossfire, as Godzilla can't just swoop down from the sky like Gamera can.
Having said that, if the next movie did have a foe, it might be neat if that foe could fly, so it could pick up Godzilla and drop him suddenly into, say, Ginza. It might also be neat if that sequence could introduce the enemy monster, rather than have an 'emergence' or 'appearance' scene they usually get - y'know, make it a real bolt from the blue.
That, or get Yumiko Shaku back.
"Crossing into established events is strictly forbidden. Except for cheap tricks."
- The Tenth Doctor, Smith and Jones