I don't have any fish in my pond and I don't put anything into it other than water. But there are lots of tadpoles and small life in the pond that just showed up. It is under trees so it gets a lot of leaves in the fall, which I clean out every few years.
The waste from your fish plus uneaten food will increase the amount of suspended algae. So your proportion of plants will probably need to be higher than mine.
I know that people do calculations to determine the size of the biofilter based on the pond size, number/size of fish, etc. But I would probably just make it a little bigger than you think you might need, and/or make your filter expandable by daisy chaining several drums together or something like that.
I pretty firmly believe that the plant roots are way more important than the lava rock or biofilter balls etc. I don't think it matters much whether the plants are in the biofilter or in the pond itself, as long as oxygenated water is moving through the plant roots. So you might think about ways to be able to keep adding plants until the algae disappears.
Here's the intake filter that I use with my pump:
Yours will obviously need to be bigger but I like this general style. I only clean it once a year. Note that this filter does not filter suspended algae - it just prevents the pump from getting clogged.
As you mentioned, shading the pond will be good for water quality and to keep from cooking your fish.
I also encourage you to include some moisture-loving flowering or edible plants in your pond and/or biofilter. It is great to have a "garden" in my pond that I don't have to worry about watering even on the hottest days or if I'm on vacation. And of course the water has a lot of nutrients that the plants like, so no fertilizing either. You just need to be able to adjust the height of the pot (or the water) to the plant's liking. I have drowned a few plants by not getting that right. And of course if you're going to be gone a long time, you'll need an automated way (or a neighbor) to top it off. My drip system puts a little water in it every day, but you could also use a float valve.
Also a word about duckweed - I once put some in because I thought it would keep the water cooler. Within days it covered the entire pond, and the frogs etc. seemed to be struggling to navigate through it, plus it made my pond just look like a lawn. So I used a strainer to strain it all out. It took a long time because you have to get every single plant.
I have attached some more recent photos without the "Photobucket" watermark.