You will need a set of good quality pans (as expensive as you can afford), decent knives and a good sharpener. Mixing bowls of different sizes, measuring jug (at least 2 of different sizes), weighing scales, measuring spoons are useful. A selection of oven proof casseroles, baking dishes etc, again of differrent sizes, also roasting tins, baking sheets, rolling pin, cheese grater (also microplane graters are useful). Wooden spoons, fish slices, carving fork, spatulas, tin opener, whisks, tablespoons, dessert spoon, teaspoon will be needed. Other equipment you can gather as you go along, like different sorts of cake tins and other utensils. Buy them whenever your recipe requires them, and soon your kitchen will be well equipped. Try not to gather lots of gadgets unless you are sure you will use them more than once.
Electrical items are not essential as most things can be done without them, but they can be useful if you are short of time. Handheld blenders are good, food processors are handy but if you only have a small kitchen your storage space will be at a premium, and these sort of items take up a lot of space.
Mainly the best advice I can give is buy what you need when you need it, my kitchen is full of stuff I thought would be useful, but that have never been used!