My personal view, and one that is unlikely to be shared by many on here, is that I don't like pockets on shirts. Or rather, pockets on shirts are invariably in the wrong place. Breast pockets, are exactly that, pockets on the breast area. Which is awkward, and mean you can't get that much in them, or I end up unable to see my feet...
Kangaroo pockets invariably end up exactly where my backpack waist strap goes, rendering them useless...
I do tend to prefer long sleeves, as I can always roll them up, but there is usually a small slit behind the cuff on the forearm for which stinging nettles have spent many millennia evolving the ability to seek out and sting...
Currently, in summer I wear a German army shirt that has been dyed black (I bought it that colour), I tend to wear it as an over shirt, rather than an actual shirt, usually with a strappy top or t-shirt underneath. As long as I don't do it up, I can put small things in the pockets, but if I bend over they do all fall out...
But, having said all this, I have a very different body shape to you (assuming that's you in the picture), and my requirements for clothing are fundamentally different from your own...
I have pondered the idea of a shirt with a pocket on the upper sleeve that is the right size for a small IDF dressing...
Julia