Ideally, the capture area of a cooktop hood should overlap the cooktop sufficiently to encompass the rising and expanding cooking plumes generated by cooking. This means that the amount of overlap will depend on the distance between pan and hood entry aperture. For distances between 30 and 36 inches, a 3-inch overlap (of the physical cooktop) all around is usually considered sufficient (and reasonable).

More technically, one wants to capture at least a 10-degree-from-vertical cone originating at the edges of all the pans/pots that might be generating cooking effluent plumes. Hence, higher mounted commercial hoods (typically at 7 feet from the floor) provide larger overlaps. Also, beyond the nominal 10-degree cone angle, larger cooktop-to-hood gaps allow greater plume disturbance by drafts, and this suggests going even wider when the gap is large.

Note that capture does not ensure containment. The airflow into the hood aperture has to be sufficient to entrain the plume and pass it through the baffles. An entry aperture velocity of 90 ft/min is recommended, and this implies that the actual achieved CFM be 90 times the area of the entry aperture in square feet.

Blower sizing requires compensating for the pressure losses the blower has to deal with from intake to outside and back to inside. Without further information, I suggest using a blower rated (at zero static pressure) at 1.5X the CFM value calculated per the directions above.

As recent posts by @opaone have emphasized, if one's cooking style includes transient plume releases, it is also necessary to have some capture volume below the baffles to "smooth out" the effluent flow rate to achieve full containment and avoid plume spillage out of the hood.

There are several other factors that need to be addressed with kitchen ventilation, and I encourage review of the many hood and MUA threads on this forum.

Your hood needs to be a minimum of 42” wide, and 27” deep. Stainless will be MUCH cheaper. A correctly done wood hood that size is easily 5-8K.

Refer to the range manufacturers installation instructions. It will indicate minimum distances from top of cooking surface (typically 36") to bottom of combustible and noncombustible cabinets above and usually also addresses the 3-6" spaces to each side and to the rear. It also usually addresses minimum CFM.

Keep in mind that the minimums the Mfr says are the worst that you can do and still be legal. If your families health is important to you then you may want better. If you don’t like the stale odors of meals past then you may want better.