Brilliant!
If you are prcessing lots and lots of clay it is worth investing the time and material to make sturdy proper screens of course, building them to the size that fits your need.
I ended up using the fruit crates because I had them around and they seemed to work fine. It's how I screen
compost and old manure for my potted plants, so it was my first thought... the idea WAS to build proper screens (exactly like the one in the picture, maybe to the size of my smallest weelbarrow), but in the end, I just didn't feel the need for them
But I am ok with working slowly in small-ish batches... it might not be ideal for everyone.
It also depends on the clay, and the way you worked it previously... I mean, I dug it up myself, and pulled most of the larger stones out while shovelling, so I am not likely to dump a small boulder in my fragile plastic screen

Most of the stuff that I need to screen is just smaller stones, twigs and pine needles (and, the horror, the occasional glass shard, because poeple used to live here decades ago! So I always have to be careful with every batch, when I first knead it, by hand or foot).
What I noticed is, that working with your tools every day, you come to know them and do things that you never thought of.
You develop processes in very unexpected ways. . Like, I noticed, for drying up over-liquid clay slurry, I can pour it in some slightly damaged buckets. I have two or three buckets that have split at the bottom but are still "whole". The thin split lets out the water but not the clay.

It's not something you can plan ahead, they must be split just right, lol.
So my advice is to experiment with what you have at hand, and then improve as needed. It's amazing how little you might actually need if you are ok with working slowly.
Here
https://www.flickr.com/photos/mihara-kokonoe-tama/36029933563/in/dateposted-public/ you can see how my clay looks when it is wetted "just right" for screening and working.

I will try to upload more pics of my project.