If your enclosing it in cabinetry you want a hood "insert" which is designed to go into cabinetry.
Physical size and cfm determine how well it works.
The size of the hood should be at leaste 6" widider than the cooking surface and no less than 27" deep front to back. That wwould typically be set at 30" above the cooking surface. If you wish to go higher it is a good idea to increase the size. Increasing the cfm does little to offset increased height.
CFM is determined by heat output- higher btu's mean. Higher cfm (don't know the metric for cubic feet per minute)
Having more cfm than you need can make for a quiter hood so lng as it has multiple speeds.
See what is available to you and post it here to see if someone has had one.