A bog is the best solution for most ponds, but if you're seeking a mechanical filtration solution, for a small patio pond, a box filter (like
https://creativepumps.com.au/product/creative-pumps/in-pond-biological-tray-filter/) in front of the pump as a mechanical filter combined with bio-media in the waterfall box as a bio-filter is pretty standard, but I don't know how big your pond actually is. You need to look for pond pumps that say for waterfalls (or for features) and that are made to move the correct amount of water and which will provide enough force to make your waterfall flowrate sufficient. You really must calculate how many liters are in your pond to choose a good pump/filter solution. It is impossible for me to give you links to appropriate pumps if I don't know how big the pond is. I know you said it's 1x1.5 meters, but you didn't say how deep the water is. If you tell us how deep the pond is, we can calculate the proper size pump. We also need to know how high above the pump the waterfall will be and how wide the waterfall box weir is. This Australian pond store has many good pump options that will work for your pond once we know exactly how much water it holds and how high and wide your waterfall is:
https://creativepumps.com.au/products/pond-products/pond-pumps/feature-pond-pumps/. Just tell us the actual volume of your pond or give us all the dimensions so we can calculate it for you, and tell us how wide your waterfall will be and how high above the pump it will be placed (how far above the water in the pond the waterfall will be also works once we know how deep the pond is) and how much flow you want it to have (gentle flow versus a rushing waterfall) and we can help you pick good filtration and pump options. A pressure filter (which is similar to a aquarium canister filter but made for outdoors and ponds) is a more expensive but more robust option. You still need a pump to push the water through it, they do not come with built in pumps:
https://creativepumps.com.au/products/pond-products/pond-filters/pressure-pond-filters/. Additionally, it's still a good idea to have a box filter in front of the pump as a pre-filter, but just putting the pump in a mesh bag can work so long as you do not have many leaves falling into the pond. IMO, it would be overkill for your patio pond unless it's way deeper than it looks.