Most of what a health inspector requires comes from the FDA Food Code, which nearly every state adopts. The exact list depends on your menu and your local authority (AHJ), but a cooking kitchen almost always needs all of the following. Your equipment layout goes into plan review before you open.
Also required in most kitchens: a mop / service sink, a mechanical exhaust hood (Type I over grease- or smoke-producing equipment), adequate hot water, indirect waste / air gaps on food and warewashing equipment, and a grease interceptor where the local plumbing code requires it. A certified food protection manager (e.g. ServSafe) is required in most states.
Sink minimums, grease-trap sizing, plan-review triggers and who issues your permit vary by state and county. See requirements by state →