I think most of the swimming ponds built in the uk and probably the eu use the Austrian Biotop system this is quite involved so would probably be described as a lot of filtering. They may well work but they are also expensive.
I used the airpump system championed by David Pagan Butler this uses airpumps around the pond connected to perforated pipe set into the gravel bed. The air pumps are run from a single 60w air compressor, this system moves a lot of water for little energy. The water quality has been excellent but its probably not for everyone. I like the pondyness of it but then i like swimming in rivers 🤔
If this was 6weeks ago I would have reported no issues however there is currently a flush of algae although the water is still clear. This has almost certainly been caused by the accidental introduction of sticklebacks. The sticklebacks eat the daphnia which eat the algae. I am currently looking at my options for removing them. Any ideas?