My o2 I maintain a lot of homes with ponds from Small 300 gal to huge 80,000 gal.
You can spend a ton of money on filtration systems but I have found nature works pretty well. Build a bog at the top put a grid of perforated pipe 1.5"-2" at the bottom of it put 10"-12" of lava rock, if you can get it, and pump 25% of your pond volume through that line per hour. Seed it with beneficial bacteria and plant it with beautiful oxygenating plants. I will try and get a picture of one I have done. It works great. I would still put in a skimmer and try and keep the water moving to pull the laves to the skimmer before they sink. The fish will also like the water movement.
If you want plants and Koi design areas that you can screen off like small coves so that the fish can't entirely get into them only eat at the edges.
You probably know this already but keep your Willow roots away from any concrete. Willows win every time.