The size pump might depend on the type fish you keep.
Other than just filtration, a pump provides water movement and oxygen exchange.
Some fish require higher oxygen levels, and more water movement than others.
I kept cichlids that out grew my tanks in a 1000 gal kiddy pool, and used a 2400GPH pond pump
My riverine species preferred heavy movement.
The generic aquarium exchange thru filtration is often considered 5 times turnover per hour, but for some species that might be too raucous, for others not enough.
Whether your water change schedule will be enough, would determined by the stocking level, and nitrate buildup, normal filtration doesn't do much for nitrate reduction, and if the pond is lightly stocked 2 gallons per hour water change might be sufficient, if heavily stocked, it might not be.