I love this thread because it goes to show that there isn't just one way. Every has their own "must do" or "must never ever do", and they all contradict each other. So here's my 2 cents, and my recipe. Find a recipe you love, and follow it exactly the first time. Some people like cookies crunchy, or chewy, or cakey, and not every recipe is going to be the perfect one for your tastes. I like chewy, so that's what I make, and get absolute rave reviews from chewy cookie lovers.
Butter - whatever is on sale - store brand is fine, unsalted. If your recipe calls for room temp, it's best to do it on the counter. Mine uses melted, which I love because I don't have to wait for it to sit out.
Salt - I use fine sea salt, but regular table salt will do.
Brown - dark.
Eggs - I usually have large, but for a regular single batch it wont change it drastically if you have extra large. While room temp eggs are good for baking, if I don't plan ahead I use them cold and they're fine.
Mixing - most recipes call for creaming the butter with sugar. Here's where you do want to incorporate air. That's what creaming the butter is. I also mix a good amount after the eggs go in. The point that you never ever want to over mix is when the flour goes in. Mix it on low until you can't see white flour any more and then stop. You don't want to mess with the gluten texture.
And of course, make sure your ingredients are fresh, like the baking soda.
I also very much concur with the poster above who cited the NY Times piece about letting your dough rest overnight if possible, but again, if I'm in a rush I don't and they're still wonderful.
Here's the recipe I swear by -
http://allrecipes.com/recipe/best-big-fat-chewy-chocolate-chip-cookie/
Since the butter goes in melted, I just mix the butter and sugar for a minute or so. After the eggs and next additions I mix for several minutes until creamy looking. Then the dry ingredients only briefly. Get a good oven thermometer, to make sure you're making at the right temp (they cost about $3). And don't over bake - they never look quite done when they are, and they will settle down for another couple of minutes after baking.
If all of your baking consistently fails you, try recipes that call for weighing instead of measuring and see how that works. And definitely try the oven thermometer.