Every cooking and baking web site lists (usually in time for a gift-giving holiday like Christmas, Mother's Day, Valentines Day or Arbor Day — hey, it has a Charlie Brown special!) "25 Must-Have Tools" or "10 Appliances You Can't Live Without!" Let's cut to the chase. There are few things that every baker must have. What you bake and how often determines what you need.
Basic
Below are the absolute basic equipment every baker must have. Note how short a list it is! Stay away from the high-end, national equipment chains that supply trophy kitchens. When you start baking, you need only a few items — measuring cups, spoons, mixing bowls, a mixer, a scraper, pans, potholders, and a timer.
Measuring cups
One set of cups in 1/4, 1/3, 1/2 and 1 cup measures for dry ingredients, and a pyrex 1- or 2-cup measure for liquids. Odd sizes like 1/8, 2/3 and 3/4 cup can sometimes be found. I like my Oxo cups; they are sturdy and have easy-to-read measurements.
Measuring spoons
One set of spoons in 1/4, 1/2 and 1 teaspoon (tsp or t), and 1 tablespoon (Tbs or T). Some sets also have odd sizes like 1/8 teaspoon and 1/2 tablespoon. Three teaspoons are one tablespoon, so 1 1/2 teaspoons are 1/2 tablespoon. The Oxo measuring spoons have the same virtues as their measuring cups: sturdy and easy to read. However, the round bowls don't fit into some spice jars, and narrow spoons work better.
Bowls
They're not just for mixing any more! In addition to a three-quart bowl and two-quart bowl for mixing, smaller bowls for holding pre-measured ingredients, cracking eggs, holding cookie decorations. As lovely as a graduated set of nesting mixing bowls from 1/4 cup to 4 quarts is, cereal bowls and coffee cups (not mugs) do just as well.
Mixer
Technically, you could do it the way your great-grandmother did, and beat everything by hand with a wooden spoon. This could be as simple as an egg-beater from the hardware store, which is capable of creaming butter and whipping egg whites. The Oxo brand has a nice, smooth action. More likely, you'll pick up a three- or five-speed hand mixer, which is even better at creaming and whipping. A hand mixer is not powerful enough for bread dough, and some cookie doughs need to be finished with hand folding.
Spatula/scraper
While not necessary, a silicone spatula mixes, folds, beats and gets the last bits of pancake batter onto the griddle. There are mini-srapers and large spoon-ulas, but starting out, a mid-sized spatula gives the most bang for the buck. Silicone lasts longer than rubber, and can be used on hot pans without making a gooey mess.
Pans
It all depends on what you want to bake. In general, your pans should be shiny (because dark colors absorb more heat and lead to burning) and heavy weight (to transfer heat more easily). Pyrex is a bad choice except for a pie plate (nine to ten inches), because the food will burn too easily. Insulated cookie sheets were the hot thing a decade ago, but bakers have cooled in their appreciation of late. If you have two of anything (two cake pans, two cookie sheets) they should be identical, so that baking times are identical. Some things are most useful in twos: cake pans (nine inch diameter is a good, generic size), cookie sheets, muffin/cupcake tins, small loaf pans.
Potholders
Ovens are hot.
Timer
I almost forgot to include a timer in this list, which is fitting considering how often I forget to set the timer. A clock works, but doesn't grab your attention when you get sucked into blogs. The timer on a cell phone or computer works, but it's much cheaper to replace a plastic timer than a cell phone.
Not-so-basic
When you know you like to bake and you've got some skills, then it's time to expand those "basic" tools. Much of what you'll use depends on what you bake. What follows are tools that, if not used every time I bake, I use often.
Parchment paper
Parchment paper is so darn useful it should almost go into the basic tool section. Not even meringues will stick to it. It's paper and can be trimmed to fit any flat-bottomed pan. It stands up to multiple bakings and can be re-used for sheet after sheet of cookies.
Extras, extras, extras
Personally, I find a second (and third, and fourth) set of measuring cups and spoons very handy, along with extra bowls and spatulas (see below for that). When baking more than one recipe at a time (say, Christmas cookies), it's much easier to grab a clean measuring teaspoon or mixing bowl instead of running to the sink to wash something off. Secondly, if you worry about cross-contamination of allergens — and everything is an allergen — you'll often use three half-teaspoon measures in one recipe. Anything you find yourself washing mid-baking is worthwhile to have a spare of.
Whisks
Not just for whipping cream and egg whites, whisks are the best tool for thoroughly mixing ingredients, either thinner batters or even dry ingredients to eliminate clumps of baking powder, cocoa or brown sugar. Whisks are even useful in cooking, for salad dressings and sauces.
Sieve
Older recipes say to sift flour with other ingredients to combine them, but whisking is better at combining. Sieves, on the other hand, are also good at getting the lumps out of cocoa and brown sugar, and draining pasta.
Good knives
Even baking requires knife work; make your life easier and buy good knives. For performance to price oomph, check out Victorinox's plastic-handled knives; they had a good review in _Cook's Illustrated_ and I've been using mine for decades. While baking I use: a fourteen-inch serrated knife to "torte" cakes, that is, cut a cake into layers; a ten-inch wide-serrated blade to slice breads and cakes; a chef's knife to chop ingredients and halve lemons and oranges for juicing; and a paring knife to slice apples and cut out pits from stone fruits.
Spatulas
Expand your spatula collection beyond the all-purpose medium size. As much as possible, stick with silicon blades and handles that can go through the dishwasher. Get a smaller size for getting into jars (get that last sticky bit into that one-quarter cup measure), a larger "spoonula" for scraping out large blobs of whipped cream or egg whites, and a Viennese spatula for folding and frosting.
Pastry cutter
If you make pie crust, scones, biscuits or anything with butter "cut in" to flour, the easiest way is with the pastry cutter. I like the wire kind, because it gets into the corners better.
Rolling pin
Either a French rolling pin without handles, or a large-diameter pin that will keep your knuckles from dragging in the dough. Wooden, because at a large enough diameter, marble will be insanely heavy.
Advanced
When your friends think you are hard-core, then it's time for tools that are investments: the stand mixer, a scale, silpat sheets, small containers to freeze leftover egg yolks, whites and lemon juice. Do you need them? Not like you need an oven, but they make baking easier.
Upgrade
By now you've been baking for years, and while the cheap things you bought when first starting out might still work, buying better equipment will make baking easier and more efficient. After 15 years of baking, I replaced all my baking pans with identical, shiny, heavy aluminum pans from Chicago Metallic: two large loaf pans, two cupcake pans, three rimmed baking sheets. I kept my heavy Wilton cake pans size 5 to 12 inches. I also stopped using my Oster blender which had such a bad design that it could not blend, and got a Kitchen Aid three speed blender.
Stand Mixer
The biggest upgrade is the stand mixer. In Europe, with those nice 220 Volt outlets, a hand mixer can power through kneading bread dough or making a batch of Springerle. In America, with our 120 Volt outlets, hand mixers can't cut it for a double batch of cookie dough. (Some stand mixers can't cut it either.) If you make large batches of bread, or wedding cakes, or Springerle and Pfeffernüsse, or bake every day, then consider a stand mixer. I have the (now discontinued) 4.5-quart Kitchen Aid, with the more powerful motor. It's 21 years old. I've considered upgrading, but it meets my needs, and it was a present from my now-husband — the best present I've ever gotten.
Scale
My first scale was bought solely to bake from my German aunts' recipes, because the rest of the world bakes by weight. When I give American cookbooks to German friends and family, I also give a set of American measuring cups and spoons. I find measuring by weight so much easier that I'll even do the math in my head for flour, sugar and cocoa if the recipe doesn't specify. Most people are not that geeky, but if you have many baking books with measurements by weight and you liked the measuring part of high school chemistry, go for it.
Silpat
Does the same thing as parchment paper, but you don't throw it out. And, you can't cut it to size. On the other hand, you buy one silpat per baking sheet, and you don't run out of pan liners halfway through the Christmas cookies. At this point, I must say that I do not own a Silpat, I own what the Germans call Dauerbackfolie (more-or-less: long-lasting baking film/foil), which had the same purpose, is flexible enough to be rolled into a tube, can be cut, and costs less.
Freeze your leftovers
As much as I try to balance making meringue cookies with making anything that calls for just yolks, I often have leftover whites, or yolks, or citrus zest or citrus juice. I hate throwing out anything I expect to have a use for later. My solution is a dozen half-cup and quarter-cup (4 and 2 fluid ounce) plastic container that I can freeze. To be honest, there is usually both a container of yolks and a container of whites in my freezer. You can't defrost the egg yolks or whites in the microwave. The yolks will solidify in freezing. Professionals avoid this by adding sugar; I just use them in cakes or cookies, where the texture won't be apparent. But it's great to pull out nearly as many frozen whites from the freezer as I'll need for the Haselnussbrötchen or forgotten cookies.
Food processor
At least half of my Christmas baking uses ground nuts. In America, you just can't buy ground nuts easily, unless you shop on line. Knee deep in the Christmas baking and suddenly short a bag of pecans, I don't have two days to wait for someone to ship me some ground nuts. Whole nuts also last longer, and are more versatile. Essentially, my food processor exists to grind nuts. It's good for other things too, like grinding chocolate, making pie crust, grinding meat, and taking up space. For grating I prefer the box grater. For thin slicing I prefer my slicer. For soups and milkshakes I prefer the blender.
Zester and reamer
While a fork can juice one lemon or lime effectively, a reamer or juicer is more efficient. Plastic is the least effective material for a reamer. My grandmother's glass reamer still has a nice edge on the ridges that does a good job of scraping and bursting the pulp. The Amco brand citrus presses are supposed to be very quick and extract a lot of juice; a cocktail expert friend uses one for his parties. If you prefer lemon or orange zest to extract, you'll also want a zester that can finely shave citrus peel. As cliched as it is, the Microplane works very, very well and makes fine zest. Other zesters are designed to make a longer, thicker zest. They take a lot of hand strength and time. And don't confuse that with the part used to cut a "twist" of peel for a cocktail. Mmmmmm. Cocktails.