Baking soda {bicarbonate soda} & baking powder - acts as raising agents. keep in the freezer/fridge, it gives you an extra year to your expiry date, especially if you hardly bake.
Salt - usually only a pinch of salt is added to your batter. Omit it though if you're using salted butter.
Unsalted butter - best for baking, as it allows you to control how much salt you want to put in. usually the butter is soften first, by bringing it out of the fridge at least 30 minutes (depending on weather) before you plan to use it, unless the recipe states to use cold butter. of course, kept in the fridge.
Caster sugar - to add sweetness, though you can use other types of sugar too {ie: molasses, honey, brown sugar, raw sugar, corn syrup (light or dark), maple syrup and many more - you have to know the correct amount to substitute, if you're planning to replace the different types of sugar in your baking.
Light brown sugar - to add sweetness. makes your goods fudgier, makes chewy cookies and the sweetness is deeper and more aromatic compared to just using caster sugar. often used in cookie recipes.
Dry instant yeast - this is good enough, you do not have to get the fresh yeast, used in bread making usually. Keep in the fridge, it last longer.
Eggs - can also act as a raising agent, as some recipe doesn't use baking powder or soda. usually you use your eggs at room temperature. if you're short of time, and your eggs came from the fridge, just soak it in warm water for 5 minutes, it'll warm it up. Best to buy in bulk (2.5 dozen), if you bake often, it's cheaper.
Vanilla extract/Vanilla bean - best to use the pure stuff, it does make a difference. Of course, if money permits, use Vanilla bean instead. You can make vanilla sugar by cleaning used vanilla bean, dry it properly and keeping it in a jar of sugar. store in pantry.
Chocolate - have 2 types, chocolate block/bar and chocolate chips. get the good stuff. Best to have a few kinds too - chips (dark, milk and white), block (at least 60% if you can find, otherwise 75% makes good chocolate goods, and you can have the usual milk and white if you want). store in pantry, please do not store in the fridge.
Milk - use full cream milk, unless recipe states otherwise, usually used at room temperature too, otherwise it might shock the other ingredients when mixed together. if you hardly use milk at home, get the long life milk, therefore, you'll always have it at hand. but once opened, you've got to keep it in the fridge.
Cocoa powder - best if you can get your hands on dutch cocoa powder, otherwise cocoa powder is good enough. there are many types (sweetened, unsweetened). I usually have a few types, as I interchange them according to how I want my baked goods to taste.
Icing sugar (confectionary sugar) - used when making icing/frosting. you really need to sift it though! if you're lazy, there are 2 ways to sifting it instead of using a sieve. {1: food processor, 2: ziplock & rolling pin}.
Oil - some recipes (ie: cakes, muffins, cupcakes) call for oil instead of butter, so keep a bottle of Canola oil at hand.
Peanut butter - who doesn't love peanut butter, of course unless you're allergic to nuts! often used in recipes. crunchy or smooth, it's all up to you. doesn't matter.
Optional
These are the ingredients that are not used often to keep stock, but rather just buy when needed. though I will also include ingredients that you can still have, but it isn't used often.
Cream - fresh cream, thickened cream {ganache, whipped cream}, sour cream {added into cheesecakes, chocolate cake}.
Cheese - cream cheese (cheesecake), mascarpone (Tiramisu) and so on. used at room temperature.
Cream of tartar - very seldom you would need to use this, but it is good to have it when you need it, keep it in the freezer - stays fresh longer. used in meringues (helps to stabilise the egg whites), sometimes cheesecakes too.
Flour - cake flour (sponge, cupcakes), bread flour (bread), almond flour (almond meal/ground almond {ie: Macarons} - gluten free), cornflour (added into some biscuit recipes, cake, custard), you can keep them in the fridge/freezer, if you hardly use them, it keep moisture out too.
Fruits - fresh strawberries, blueberries, raspberries. though you can also use frozen fruits if you prefer to always have some at hand, though use fresh fruits if it isn't going to be baked!
Food colouring - if a recipe {ie: cakes, icing, biscuits} calls for colours to be added, best to have the powdered colours, as the colours turn out better, and gel paste form. it doesn't affect the ratio in your other ingredients too. best to avoid liquid colouring (as it might add too much liquid into your recipe).
Nuts - Almonds, Macadamia, Hazelnuts, Pecans, Walnuts, Peanuts, Pistachio and many other. store in air-tight containers and it can also be kept in the fridge (keeps moisture out).
Lemon - best to have the fresh stuff, but if not, just keep a lemon juice bottle in your fridge. helps to enhance the cheesecake flavour and of course other types of good too if you like the lemon taste.
Spices - cinnamon, mixed spice, nutmeg, ground ginger (ie: used in gingerbread cookies/bread).
Sprinkles - 100 thousands, nonpareils, candies and other colourful decoration sprinkles to decorate your cakes, cookies, muffins, cupcakes.
Instant rolled oats - used in making biscuits, mueslis and so on.
There are so many optional ingredients that you can have, but these are my take on what you must have and may have. If there are any ingredients, you're unsure or would like to add to my list. just comment below.