It depends. Traditionally cast-iron did not come pre-seasoned.
Lodge, as you know, specializes in pre-seasoned and enameled cast-iron pans. Lodge pans work great, but there isn't anything exceedingly special about their seasoning; it's simply vegetable oil (soy) baked onto the pan. You should be able to achieve a similar seasoning quality at home using the methods described here:
What's the best way to season a cast iron skillet?
Wagner skillets do not come pre-seasoned from the manufacturer. However, they did typically come with some coating in place to prevent rusting. This coating, while safe, is not intended to be a "seasoning". It wears off over time, and it's role is subsequently filled by proper seasoning.
Update
Based on your photos, that looks to be the coating I described above.
What is the advantage of a steel skillet over a cast iron one? I currently use cast iron for most everything and am curious what I might be missing.
Pan sauces made with wine, vinegar, or any other acid are better in stainless steel. If you put any acid in cast-iron, you are harming your seasoning, and leeching iron into your food. This will affect the taste of your sauces, I find pan sauces taste metallic when made in cast iron.
Stainless steel also heats up and cools down much faster than cast-iron. This is great when you need quick heat, or fine control of your heat. You can also plunge a piping hot stainless pan into an ice-bath without cracking it in half.
If there's an advantage to getting a steel skillet as well, what would be recommended?
Go with a a bonded stainless-steel pan with an aluminum core. The most well known manufacturer is All-Clad. The stainless steel exterior is great due to it's non reactivity, you can literally put anything in it. The aluminum core distributes the heat much more quickly and evenly, minimizing hot-spots.
Is a steel skillet good for cooking omelettes?
Not in my opinion. I go with a non-stick pan every time.
I have to recommend sticking with a nonstick pan for eggs. There's simply nothing better, although well seasoned cast iron comes awful close. If you're spending more than $20 for a nonstick egg pan, you're doing it wrong. You don't need Calphalon, or any other big name for a good nonstick pan. Go to a restaurant supply store if you can and buy a cheap one there. With care it should last you 2-5 years depending on use. I found my current one at a Bed Bath & Beyond.
Best Answer
The bottom of the 8" pan is a bit less than half the size.
For a 2" deep-dish, there's a 2-inch high (if you take it to the top) 8π circumferential strip for another 16π, and presumably the 12" dough is for a flat pizza. At 32π .vs. 36π I'd do the whole box, unless your deep dish isn't really all that deep.
I'm also a bit concerned about the "never used" cast iron pan needing some seasoning, but perhaps it's "lodge logic" pre-seasoned.