Your best choice for a pan depends on what you want the pan to do. There is no single, best choice. There may not even be a single best choice for you.
If you plan on making lots of omelettes, you defeat yourself with a saute pan (aka chicken fryer), or any other straight or high sided pan for that matter. In fact, if you plan on making eggs at all -- a straight sided pan is not your friend.
A slope sided pan makes it much easier to introduce a spatula -- especially around the edges. You could say I disagree with Chris and KY about the superiority of straight sides -- at least until you get into larger pans.
The best size pan is one that will closely hold the amount of food you want to cook, without crowding. The right size pan is VERY IMPORTANT for sauteing, searing, and a few other pan techniques.
Stainless steel will not "get more heat into the pan." Meaning no offense, that's just gibberish unless you were previously cooking in wood.
Stainless steel is useful at the heart of any pan set because it's non-reactive. That is, you can safely long cook highly acidic and reactive foods -- such as wine sauces, artichokes, etc. Other choices like pure aluminum, carbon steel, cast iron, may be used for cooking these foods, but only for fairly short time periods. Although I prefer carbon steel for most cooking, it's important to have something non-reactive at the core of my set.
Modern, multi-ply stainless steel is an excellent choice because it combines non-reactive stainless interiors with high-performing bodies. It is almost certainly your best choice for your core set.
Lids. You can get lids in pretty much any size you want a lid. It's nice to have at least one lid for every size pot or pan you own. Don't forget -- there are a lot of things hanging about the kitchen which make perfectly good lids -- plates, for instance.
I suggest a 12" saute pan, and a 10" and 8" skillet for your first pans. That covers most of the bases for these types of pans.
If you can only afford one pan, get the 10" skillet first. It's a pan that a single or couple uses almost every day. Unless you always cook for four or more, a 12" (or even a 28cm, for that matter) is too big to have as your only decent pan.