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