Usually you position the hood at the lowest height to grill surface 18"-21" from deck top to underside of exhaust unit. Like a microwave over a range, the base of the unit should actually not sit flush with the adjoining cabinets, 3" higher is the modus operandi. The reasoning being the heat and also the additional benefit of being able to all the grill/range that you're cooking on.
Add'l height can also be adjusted based upon the cfm of the mechanical exhaust fan in side the hood liner. So is your hood a simple chimney or is there a mechanical component? Is the grill gas, charcoal or a combination of both?
They also have units that raise up from under the counter top behind the grill that do back venting and then can be lowered to be concealed. Exhaust piping is a whole nother animal that then runs thru your base cabinets to the outside.
