If I'm going to invest in one skillet for everyday use (sautéing, simmering, frying), what do you recommend?

Cast Iron all the way! NEVER non stick pans! BUT make sure you know how to properly clean and season them. They brown foods wonderfully, great conductor of heat, versatile on stove top and oven and cheap price wise.

I would recommend you to use only authentic brand skillet because they are commonly used in our everyday life for sauteing, frying, etc. These kind of cooking can only be done in a better way if you use nonstick skillet. If you don't mind i would like to share with you the two varieties of saute pans which i use for cooking and they work fine. one is Nonstick Saute Pan with Cover and Helper Handle and the other is Best Hard Anodized Cookware – T-fal Ultimate Fry Pan

I have my mother's and grandmother's cast iron. They have stood up to time and to heavy use by three cooks and still work perfectly. I wouldn't think of giving them up. I came across a high-end skillet in the thrift shop years ago and snapped it up. It quickly found its way to the bottom of the closet, where it has stayed undisturbed. If I were you, I would look in yard sales for old cast iron. I am fairly certain that the newer models are made in China and are inferior.

You need more than one. Invest in three. A ski pining sided AlClad skillet, a Scan Pan or Diamond brand medium size non stick skillet
and a medium size Lodge cast iron.

I use my cast iron skillet everyday.
Inexpensive and lasts forever.

For non-stick, I adore my Aeternum: http://www.bialetti.com/aeternum-collection/. They hold up really well, they don't flake or emit hormone-interrupters like teflon, and they are relatively inexpensive. When I don't want non-stick, it's All Clad all the way. They are pricey, but worth it if you can swing it. I bought my set 13 years ago and still love them. I imagine they'll hold up for the rest of my life.

If you get something really large, make sure you get a pan with a second handle. Worth every penny.

Oops! I didn't mean to "like" my own answer under Half Pint! Oh well. :-) I wanted to add a few things in addition to what I wrote before. As I said, I love that big skillet, but for my family of 3, it is not one that I use every day - too big. I have two other skillets I love: an 11" All-Clad skillet and a 13" old cast iron skillet that belonged to my uncle. It is perfectly seasoned! I really like using cast iron and it is not difficult to take care of once you know how to - there are great instructions right here on Food52. For everyday cooking, these are the two skillets I turn to. Note: neither one has a lid, however.

Cast iron. You can put it in the oven, and when it is seasoned correctly, its nearly non stick. And will last ages.

If you heat the pan correctly, any good pan is "non-stick." Coated surfaces are all composed of chemicals that may or may not get into your food... I wouldn't use one.

I like DeBuyer. Williams Sonoma sells it. You do have to heat it up after cleaning it, but food does not stick to it and it comes in various sizes. It can go in the oven up to a high temperature.

I have this one, in the 4qt size. http://www.williams-sonoma.com/products/all-clad-d5-stainless-steel-essential-pan/?pkey=ccookware-all-clad&cm_src=cookware-all-clad||NoFacet-_-NoFacet-_--_-

I love it. I use it for everything that will fit into it. This D5 series is stainless steel and non-stick. That's right non-stick. $150 is a bargain for an All-Clad D5 pan.