Kitchen wiring requirements are very strict and quite complicated.

For starters, if you truly have no existing wall outlets, you will need to provide at least 2 20a GFCI circuits for wall outlets to meet code. These cannot be used in conjunction with any other wiring.

Usually you will then need a 15a dedicated circuit each for:
dishwasher; fridge, hood fan (esp if this is a microwave/fan combo, in which case the requirement may be 20a) If you have a disposer it can be combined with the dishwasher circuit--but check your local requirements.

Cabinet lighting falls under the miscellaneous requirements, but usually it would be combined on a 15a circuit with other lighting (or even other non-GFI floor level plugs in some jurisdictions).

You cannot have any aftermarket soft cord style wiring enclosed in walls (although running it through cabinets is OK)

Depending on your configuration, you may find it easiest to locate a utility box either on the underside of the cabinet (ours have a deep recess so it is easy to do it that way), or even inside the cabinet, and install a standard double outlet and then have that outlet switched by a wall switch.

If you wanted to have two "strings" or runs of UC lights, you could add second run from the wall switch, & have each side of the plug switched separately.

The typical installer leaves some NM (Romex) cable poking through the drywall, which you would then bring in through the cabinet back into your J-box, install the outlet etc. Normally they would leave some slack and you can cut the drywall to move it up or down, once you know where you want it to come out of the wall & then patch appropriately.

If you UC lighting is low voltage (like pucks or some strips) you would then plug in the little power bricks, & run the manufacturer's low voltage wire through holes drilled in the cabinets to hook every thing up. You can keep it fairly tidy by stapling in place and bundling unused wire & zip-tying it by the transformers.

Some UC lighting is made for direct wiring--in that case the NM (Romex) wire coming through the drywall is hooked directly to the junction box on the fixture, & often the manufacturer's own wiring is used to link (by holes drilled through cabinets) to the next fixture.

But if you wanted to control the UC lights from a wall switch, it may still be easier to install an accessible junction box to collect the wall switch wire(s) and power feed from the breaker box, since usually the room provided on the U/C fixture is not large enough to add the additional wires needed for a wall switch.

If the fixtures have separate on/off switches (some do, some don't), leave them all on at the fixture, and then use the wall switch to control them.