The most basic is of equipment would be this--a pan, a knife, a bowl for mixing, and a wooden spoon.
With a good quality pan you sauté, pan fry, pan roast, stir fry, and even shallow poach.
For ingredients, just learn to cook basic proteins--beef, pork, and chicken. Eggs are a great start. Green vegetables and starches--pasta, rice, etc.
You can then learn your favorites or a particular cuisine--Italian, etc.
And get a good basic goodbook for reference. The Internet is nice, but I'm partial to cookbooks. I like How to Cook Everything or the Joy of Cooking.
PBS also has some good shows. Food Network used to good when they had chefs on, which was years ago. All the chef driven shows are on PBS or the Cooking Channel, which the Food Network owns.