Three good knives, the best you can afford. An eight inch knife for most of your chopping requirements; a utility knife with a serrated edge for tomatoes and soft fruit etc, and a three inch vegetable parer.
A bamboo end-grain chopping board. Choose end-grain so you won’t split the board. Bamboo has natural anti-bacterial properties, making it a hygienic choice, and it’s a softer wood, so it won’t blunt your knives as quickly. But never, ever put it in the dish washer – it will destroy it.
A good quality stainless steel deep frying pan. Stainless steel makes for a good, heavy-based pan and has no coating on to go wrong. It’ll give you a nice sear on your meat, and let you cook good sauces and everything like that. Copper is the chef’s choice, but not a necessity; stainless steel is cheaper and should last a lifetime.
A good cast iron casserole pot for slow cooking, or for roasting a chicken or leg of lamb, or making a bolognese. Incredibly versatile, something you can put in the oven or on the hob, and also bring to the table as it looks so nice. I do believe in investing in quality here. It’s hard to damage them, but I do know people who have. Often they’ll have made a casserole and put the whole thing in the freezer, then put it straight into the oven when they want it.
A good, non-stick omelette pan. You can buy them now with a life-time guarantee, and again, I think it’s worth investing in a good one so you get to know it and what you can do with it. As with the casserole pot, avoid thermal shock – don’t put a hot pan under the tap as soon as you’re finished with it. Let it cool first.
My top tools are a zester / rasp. I don’t like graters. Rasps are long and thin and very sharp; mine has a finer rasp end for zesting and parmesan, and a bottom end for cheese.