How should I connect a new ceiling fan which is controlled by a remote?
Connect the white wire to the white wire.

If you want the wall switch to turn off the light/fan, then hook the pink wire in the box to the black wire on your controller. If you want to prevent the switch from turning off the light/fan then connect black to black.

Which ever wire you don't use should be capped with a spare wire nut and wrapped with electrical tape.