if you're going to do an external / remote fan & ducting, check with a local sheet metal fabrication shop.
you can likely get a to the nth dimension/size stainless steel hood. with filter rack and drip pan and e-z drains, for half - or less - of the big name stuff . . .
and features you may not get in the biggie names....
btw . . . 'oversized' is a most excellent choice.
I have a 36" six burner top, with a 36" 'hood' to fit the space,
and windows with lots of 'film deposits' from hi-temp searing/frying, even on the highest fan/CFM setting....
given my 'druthers, I'd go for 8" each side and 8" front to back . . . to capture the 'issue' of real cooking.