The get off and walk eliminates a road racing shoe pedal set, because they are not made to walk on.

That leaves a recessed cleat mountain bike type shoe and pedal, or just a decent platform pedal
with toe clips to flip over, and put your shoe into [probably not a spongy sole running-shoe]

or a bigger platform pedal and what ever shoes you will wear thru the entire day ...

my Daily rider uses Ergon pedals they fall in the last category..
big surface curved so my foot stays centered over the pedal
and smooth rotating due to weather proof bushing design, for a bearing that never needs lubricating.

my daily trip is about 3~4 miles each way . :30 on average.