Great list. I'd add fresh red chillis - vit C, great taste, add colour, etc. And garlic.
Feel free to ignore this bit if it's against the 'basics' spirit of the thread, but if I were nominating some essential flavourings/seasoning/spices, apart from salt and black pepper, I'd go for whole cumin seeds, a jar of 'lazy' ginger (keeps for quite a while in the 'fridge), a block of fresh coconut (ditto), lime juice, dried parsley, oregano, turmeric, coriander leaf and basil, a small tub of vegan 'parmesan' and a bottle of soy sauce.
Together with the other ingredients mentioned you're then able to produce a big range of 'styles' of food, even if you're not being completely authentic; S Asian, Thai, Chinese, Italian, N African, etc.
Of course I'm surprised no-one's mentioned olives yet...