Trying to adapt any of the games wouldn't be the best course of action to me for two reasons: 1) Trying to pick just one story in a nearly 40 year old franchise is quite a big task and 2) I don't think any Zelda story would fit a theatrical film.

Soooo, I think Illumination is going to pull a Spiderverse/Everything Everywhere and make the Zelda movie a "multiverse" (really a time travel) movie. Basically, it'll be about Illumination Link, Zelda, and Ganondorf having work together to save the Zelda multiverse from a bigger, more malicious threat than even Ganondorf himself. It'd be a big action-adventure film with a slighty more serious tone than Mario (think How to Train your Dragon), no needle drops (it makes literally zero sense with this IP), and R E F R E N C E S. But not to nearly the same extent as the Mario movie as Mario has far more recognizable elements than Zelda.

Link wouldn't talk and would be officially diagnosed as mute. The trio would use Sheikah tech to travel to different dimensions (some possibly not even Zelda related, but rather broadly Nintendo related).

I think general audiences could get on board, and could make around $500M-$600M at the worldwide box office.

TLDR: Illumination Zelda movie would be a time traveling, dimension hoping celebration of the whole franchise rather than one game.