My guess is that 90% of it is your cookie sheet. I use commercial sheets called a half bun pan that I get at a restaurant supply. They are heavy aluminum and cost about $5.00 each. They are VASTLY superior to any other thing I've ever used. I even had some of those air sheets. And you want them bright and light, not dark in color. Dark absorbs more heat and makes the cookie browner.
Make sure they are cool between each batch. If you put a fresh batch on a hot sheet, it will spread too much and thus get overcooked and lose it's shape.
I still have trouble too, but mostly because I'm higher than Denver in altitude, but having good cookie sheets made my cookies much better.
Chocolate chip cookies, IMHO, are the easiest to make. As are oatmeal cookies, or peanut butter (I am a drop cookie fan!).
I always make them by hand - I like the process of creaming the butter and sugar together. It takes longer, but I really enjoy it. I always use butter. I always scoop my flour with a large spoon and sift slightly into the measuring cup and then level off with the back of a knife...I never scoop directly out of the bag using the measuring cup, it gets too packed down and won't give you an accurate measurement. I use heavyweight aluminum pans and always use parchment paper. I prepare 2 trays, but only bake one at a time, so that I always have something in the oven and something cooling. I bake my chocolate chip cookies for about 10-12 minutes depending on size. I let them cool slightly on the tray, and then remove them to a cooling rack.
Aha... my cookie sheets are horrible and I do live in high altitude too, Salt Lake City.
Also, if you melt rather than soften your butter, your cookies will spread. I often melt my butter (well, I use margarine, I'm cheap that way) and then once the dough is mixed, it goes back in the fridge to firm up again so it will bake right. If I'm in a hurry, I just add more flour until I get what I want.
It's ok to bake 2 or 3 cookies and see what results you get. If they spread too much, add some flour (like a handful) and mix well, then bake a few more and see.
Corinne, I am a fellow Utah girl (I remember you from the board) I'm also a bit famous for my cookies.