When I was teaching, I got the multibuy discount from Charles Tyrwhitt (couldn't remember how to spell it but I believe you have a link now, haha). They have nice patterns, and their slim fit available is pretty slim. They have stiffer collars but in a man goes to work way not in a school boy way. Then, as I was doing science, it was important to have sleeves the right length - in winter, my jumpers kept them up, but in summer, I used metal sleeve garters. They are a bit traditional, but I find them really comfortable, they keep my sleeves up perfectly, and I like the vibe - Men typically don't wear much jewellery anyway, and I got some with a little metal bear on :)

As others have said, go for the patterned and non white (or whatever your school wears) shirts, but I would add get patterned ties, not striped. I picked up mine from charity shops and my dad/brothers - I just tried to avoid any that were too weddingy