Short answer: if an appliance produces grease vapors (a fryer, griddle, charbroiler, or range), the mechanical code requires a Type I grease hood with exhaust and fire suppression. If it only produces heat or moisture with no grease (a dishwasher, some ovens), a cheaper Type II hood may be enough. Which hood you need is the single largest hidden line item for a first-time kitchen, and it is decided by what you cook, not by what you would prefer to spend.
Type I: required over anything that makes grease
The rule lives in the International Mechanical Code (IMC) §507.2. Per the adopted code text:
"A Type I hood shall be installed at or above all commercial cooking appliances and domestic cooking appliances used for commercial purposes that produce grease vapors."
The moment you put in a fryer, griddle, charbroiler, or open range, you are in Type I territory: a grease hood, grease-rated ductwork, a make-up air system, and a fire-suppression system over the line. That is why "I found a cheap used fryer" is never just the price of the fryer.
Type II: heat and moisture only, no grease
IMC §507.3 covers the lighter case:
"Type II hoods shall be installed above dishwashers and appliances that produce heat or moisture and do not produce grease or smoke as a result of the cooking process, except where the heat and moisture loads from such appliances are incorporated into the HVAC system design or into the design of a separate removal system."
A dish machine or a bakery convection oven may qualify for the cheaper Type II. A fryer never does. NFPA 96 then governs the construction, clearance, and regular cleaning of the grease exhaust system on the Type I side, which is an ongoing cost, not a one-time one.
The health-code backstop
Even once the mechanical code decides which hood, the FDA Food Code decides whether it actually works. §4-301.14:
"Ventilation hood systems and devices shall be sufficient in number and capacity to prevent grease or condensation from collecting on walls and ceilings."
So an undersized or worn hood is both a mechanical-code and a health-code problem. When you buy a space or used equipment, the hood question is the first thing to price, because retrofitting a Type I system into a room that never had one is where opening budgets blow up.
Price the appliances that drive the hood decision against their documented failure modes first: browse the model records, and see why the equipment itself must be certified.
IMC §507 text quoted from UpCodes' reproduction of the adopted 2021 International Mechanical Code; the FDA quote is from the FDA Food Code 2022.