These are the little things you'll want in a readily available place. In most cases, you'll find that the more you have of them, the better (I'm looking at you, wooden spoon!).
Stainless steel mixing bowls
Flat-end wooden spoons
Heat-proof silicone spatula
Liquid measuring cups, at least one 2-cup
Dry measuring cups
Metal measuring spoons
Maybe the most common mistake new cooks make is buying those big knife sets. I'll bet 98% of your cutting will be done with three knives. Rather than getting a bunch of mediocre blades, it's far better to spend the same amount of money but concentrate on three good ones. They'll last your lifetime.
8- to 10-inch chef's knife (6-inch Santoku, if preferred)
3- to 4-inch paring knife
Serrated bread knife
Wood or composite cutting board
Pots and pans
This category is where being a careful shopper pays off most. There are some cases — a good sauté pan and saucepans — in which it's worth spending the money to get the best quality you can afford. There are others — nonstick skillet, pasta pot — in which you're safe bargain-shopping. Because, really, who needs a $200 pot for boiling water? Generally I find baking equipment is much less variable, both in price and quality. The good stuff isn't all that expensive, and the cheaper stuff doesn't work that much worse.
8-inch nonstick skillet
10- to 12-inch (3 quart) sauté pan
5- to 6-quart cast-iron Dutch oven
8-quart pasta pot with steamer and liner
2 jelly roll pans
1 loaf pan
1 9-inch tart pan or pie plate
2 9-inch round cake pans
13-by-9-inch glass or ceramic casserole
I'd almost consider these to be more part of the pantry than equipment. You'll need lots, and you'll always run out just when you need them most. Buy backups.
Sealable plastic storage bags in various sizes (especially 1 gallon)