@alpinepaq, start here: https://bamasotan.us/range-exhaust-hood-faq/

As mentioned above you should have much greater depth than just 12". Ideally 27-30" but otherwise as large as possible. 12" is better than nothing but will still leave a lot of cooking effluent and the VOC's, Carcinogens, PM and odors that come with it in your house for you to breath.

@WizeOwl and @opaone - thanks for weighing in. I know that a smaller footprint hood isn't as ideal, but from a design point of view in our small kitchen, we're hoping to make it work.

Similar to designs like this, or this.

There are several manufacturers that make inserts for 12" cabinets, and we assume we would get a product capable of 600 CFM. For example this by XO, orthis by Faber.

Hoping someone here has had success with a smaller profile insert hood.

https://futurofuturo.com/42-insert-liner-wall-range-hood/

I have this in 42” custom cab and it works great with my range. High power, ducted, vented through the roof and not loud. Good luck.

@xyzzzz12345 - Thanks for chiming in and for pointing me to that brand. Looks somewhat promising. Can you go into any specifics of the unit's performance? Do you find it does a solid job handing the load? Do you cook frequently? What type of range? Gas or electric? Really appreciate your insight.

"@WizeOwl and @opaone - thanks for weighing in. I know that a smaller footprint hood isn't as ideal, but from a design point of view in our small kitchen, we're hoping to make it work."

Keep in mind that this is a functional element that if not done properly can result in poor indoor air quality and long-term health problems for anyone living there. 20 years of COPD, earlier onset of cognitive decline and Alzheimers along with other health problems is likely not worth 'but it looks better'.

Read the FAQ I posted.

Alpinepaq - my kitchen setup is same as your integrated hood idea photo. Range - 5 burner La Cornue. Family of 5 cook at least 2 meals daily. The key to fan is turning it on at the onset of cooking, which I typically do. The hood is reasonably quiet at highest setting. It carries odors out, non lingering after cooking. I indoor sear meats and seafood using cast iron at high heat with no issues. The distance between range and hood is 30” with soapstone slab backsplash. There is a nearby window and didn’t need a huge hood sticking out in a small city kitchen. Hope this helps.

Also, previous one before remodel was a overhead microwave that did not cover the depth of the range and not powerful enough to remove odors.

We plan to go with one of those https://www.fisherpaykel.com/us/ventilation/integrated-ventilation/

The hood should really be deeper than 12" to capture the cooking contaminates. No one will have a blower powerful enough to pull them into a 12" deep hood and not sound like a jet engine. Vent A Hood has a liner that the bottom pulls out when cooking and then can be pushed back in so it looks like a standard cabinet when not in use. Check out their TLH model.

https://ventahood.com/index.php/products/premier-magic-lung/ml-liner/ml-wm-li?id=360&model=TLH