The big cons of the kind of insert pictured in your design is that it's not deep enough to really capture fumes well. That's extra important if you have a gas cooktop. Your hood should also be 6" wider than your cooktop--can't tell from your picture whether that's the case in your design.

thank @mcarroll16, I believe the KD has a 36" range hood w/ 36" gas cooktop

For me, the questions were "how does this thing vent" and "what do I want to look at". Do you connect through the ceiling or the wall? Do your cabinets go to the ceiling? Would cabinets cover where it vents? Personally, I don't like the look where the chimney goes up through the celing but the cabinets stop two feet below or where they try to hide the vent in the cabinets but there is still a covered vent box above the cabinetry up to the ceiling. If going with a chimney, what style do you like - flat, curved, glass, all stainless, rounded, more triangular/pyramid? There are a lot of choices. If you do a chimney, where do you stop your backsplash - bottom of the chimney, top of the cabinets, ceiling??? Also, what size are the ducts you're connecting to, does it match the venting size of the hood you like? Does the hood you like vent to the top or to the back, can it be adjusted to match your connection or will you lose power due to an additional bend?

Not only should the hood overlap the cooktop side-to-side by a few inches, it should do so front-to-back. Further, there seems to be no hint that the hood performance parameters have been calculated for any design, even the inadequate sized ones shown. Is this hood system intended to avoid the need for make-up air? Does the planned usage of the cooktop exclude hot oil cooking such as meat searing or stir-frying?

Have the cooktop installation requirements been carefully reviewed to determine whether it can be mounted against the wall with island trim? Is the wall non-combustible all the way through?

@kaseki --sorry but I don't think I follow all of what you said. I am assuming when I'm ordering the cooktop and providing the item # to the KD she can make any necessary adjustments for installation requirements. I don't know what you mean about "wall with island trim"

The hood will vent outside through our garage

@kim Valid thoughts---ours is venting through the back wall, our cabinets go to the ceiling, I think I like the flat or pyramid shaped ones the best, we are doing a tile backsplash and are thinking to take the tile all the way up to the ceiling

Cooktops and ranges without back-guards are denoted as having island trim because islands don't have walls that can be overheated. Do not assume that installations such as your first and second photo are actually code compliant. If your KD is all-knowing and familiar with IMC 308.4.2, or at least checked the installation specs of the particular cooktop, then no more need be said about walls.

As for adequate ventilation, you can read numerous threads here on hoods and MUA, or the supporting literature, or depend on your KD to have done so. Presumably she asked you about cooking style, tolerance for odor and grease, etc. She should have at least informed you of the performance of potential affordable hoods, including trade-offs between aesthetics and performance where applicable.

I think it's what makes you happy. Cabinet hood ranges might not have the power if you have a large room. There are so many variables and as everyone else stated, there's so much info on-line to what will suit your style and need for your kitchen and cooking style. There is also vented and non-vented, what are the filters like and on, and on. Good luck! I've read the hood should extend two inches on each side of your range, and then a pro said, as long as you have the proper range hood, it can be the same size as your range. Which all three pictures show!