The usual stuff applies. Residential hoods assumed. En brief:

• The hood needs to overlap the cooking utensils by several inches due to plume expansion with plume rise. This applies to front to back depth as well as width. Hood base height above the cooktop between 30 and 36 inches is recommended. For higher spacing, larger hoods with more air flow rate are needed.
• The air flow rate into the hood's entry aperture should be of the order of 90 ft/min, which equates to 90 CFM per square foot of aperture. Slightly less may be sufficient with induction due to no gas plume, but that somewhat depends on cooking and whether there is much turbulence in the area from movement, a/c cross flow drafts, and make-up air (MUA) introduction.
• Assume that with baffles and MUA pressure losses, the actual flow of a blower will be about 2/3 of its rated flow.
• Duct diameter should be such that the flow velocity in the duct is between 1000 and 2000 ft/min at full power.
• If you want quiet, it is necessary to use an external or in-line blower with a silencer in the duct path between hood and blower. This suppresses blower blade tip turbulence noise and some downstream duct turbulence noise. Baffle hiss will remain.

MUA system details are another subject area to address after the Hood system details are preliminarily determined. MUA will need to be defined before ordering hood system parts due to possible interacting requirements.

Variations in lighting will be present with different hoods. I can only report from experience that my Wolf Pro Island hood is adequate in that respect with its original halogen lamps and with replacement LED lamps.

Feel free to ask about application of these rules. Review of the immense number of kitchen ventilation threads (topics) on this forum is recommended, even though it will take a significant number of hours. This is the most complicated aspect of kitchen design, in my view, unless you are learning the NEC (NFPA 70) in preparation for DIY electrical layout and installation.

For a 36"W cooktop (or range), I would get a 42"W x 24"D hood. Install no higher (or lower) than the manufacturer's specs state. As Kaseki mentioned, usually 30" to 36" above the cooking surface. Most, I think, say 30", but some allow for up to 36".

FOGSS (Fumes, Odors, Grease, Smoke, Steam) spread out as the rise, so a hood wider than the cooking surface is generally recommended, especially when there are no upper cabinets abutted the hood.

Regarding fan and MUA, see Kaseki's comments above - especially about searching the Kitchens Forum (and, maybe, the Appliances Forum) for more information.