Do an island hood, hung from the ceiling. Vent up and out.

Then it is kinda in the way of the window.... But thank you for your idea!

Thank you for the beautiful pictures! I think I would prefer under cabinet hood then... A further question, what is the min length of duct work i will need for a under cabinet hood? Trying to see whether I can fit everything it in a 30'x24'x15' cabinet or I need the duct to get through 2 cabinet. Thanks!!

You’re welcome. When you shop for your range hood, read the specifications for the unit. I doubt you would need two cabinets. Generally speaking, you want the range hood to extend beyond your range by two inches on each side for maximum functionality, but this is not required.

Melody, I'm a licensed mechanical contractor who specializes in kitchen ventilation. Your photo suggests your cooking area will back up to an exterior wall. Some hoods, but not all of them, feature the ability to rear vent vs exhausting out the top (Or immediately out the top, into the cabinet above, then out the wall) So could be mounted under a cabinet as you wish. Providing for a wider hood to facilitate vapor capture, as has been suggested, is a smart approach. A 36" hood over a 30" cooking unit looks cool, too. However, anything in the path of the duct, regardless if it's within the wall &/or on the exterior of the wall will have to be modified to provide clearance for said duct. Period. And remember hoods under 400CFM are not high-performance units. But hoods over 400CFM require make-up air be provided. Not a DIY project. Pull a permit. Good luck!

You need a better kitchen layout.

I love the clerestory windows, but you may have to do something like these pics,

Or, do like they've done here

you need 30" from the vent to the stove top.

The best look? Pic #1. stove w/a down draft. That large white range you have in the spot doesn't really work .

#2 and #3 are second.

Can you move the stove elsewhere?

I hope you plan on going w/more of mcm type of look.

It is a mid-century house! But it is pretty small. The kitchen area also include washer and dryer, the plumbing is already done so the sink is stayed at the island. Really no place to relocate the stove. I plan to just do under cabinet range hood, maybe get through the side wall can provide enough length for ducting?