A 36" cook top needs 42" insert for decent capture of odors and grease. THEN comes the desired cladding. This type of hood tends to look best in a style where cabinets butt to the hood cladding, or there are NO upper cabinets nearby.

You need the specs.....for the insert. We've no clue what style you are planning, the look of the kitchen or anything else.

We don't read minds, so you might show your kitchen plan with all the dimensions and appliances........walls windows, all of it : )) and an inspo of your desired look in the kitchen.

Drywall will be a grease nightmare so consider that as well .

Not everything is easy......

how will you finish, etc

I dislike clad hoods and for sure in drywall and painted . THe hoods get greasy and no matter how good th vent the steam from cooking also discolors the hoods over time You need to aslo consider the 2x4 construction in to the size of this monster hood by the time you are done , Sorry not helping I know but a good stainlees high CFM hood is still IMO the best choice . I also often do a hood with a bit higher CFM the same size as the range .

You need accessibility to the guts for this to be done. No part of the wood should be exposed, over the range. The insert needs to be 42"-48" and 27" deep for that to happen. And you need to understand and follow fire codes, and building codes.

Framing w/ 2x4's will result in a really bulky aesthetic. Typically a hood insert surround is made by a cabinet maker which results in fairly thin structure - think 1" v 5" thick around the edges.

As others mentioned, a 36" range should have at least a 42" wide hood - big capture/containment area is good. The cabinet structure for it then might be 45" wide. With 2x4 it'd be around 54" wide.

Wood over a range is totally fine so long as it's high enough. Grease on surfaces like hood surrounds is only a problem with insufficiant ventilation.

We have a 60" hood insert enclosed in a wood surround over a 48" range. After five years of continuous and often grease heavy cooking (lots of pan frying, wok, etc.) including lots of dinner parties and guest chefs, our wood surround still looks new.

Photos here: https://bamasotan.us/2020/12/the-kitchen/

The systems from @Fobest Range Hood are quite poorly designed.

1. They have zero containment area. Most effluent will not be captured nor exhausted.
2. Blower is in hood so will be quite loud.
3. Baffles are poorly designed. They will be noisy and may not do a good job removing grease and PM from the airstream.
4. Too shallow (front to back)
5. Blower will likely perform poorly in actual use.

Basically, all form and no function so a bad choice.