[link|https://secure.lodgemfg.com/storefront/products1.asp?idDept=1404&menu=logic|Lodge] L10SK3 12" skillet and L8SK3 10-1/4" skillet. Available at any restaurant supply or on the Internet. Cast iron is nowhere near as difficult to maintain as some people imply.

I also strongly recommend the Lodge L9OG3 10-1/2" round griddle for those doing certain ethnic cooking (best thing ever for roasting whole spices before grinding for curries, etc.).

I also recommend 2 quart and 3-1/2 quart full clad (stainless - aluminum - stainless) covered sauté pans, but not for sautéing which is best dones in a pan with low sloped sides. Note: "sauté" properly refers to a very hot short frying - not another word for "stir frying" as it is so often applied today.

These are super pans for recipes where you start out lightly frying onions and such then add liquids and cook covered, just not very good for heavy frying. I use the 2 quart constantly, the 3 quart almost as much and the 5 quart only a few times a year.

Edit: For French omelets, a 9-1/2 inch plain stamped sheet steel pan with shallowly sloping sides and a long, firmly mounted wooden handle. This is the one pan that takes special care and is washed only if you've screwed up. Any egg stuck to it is scrubbed out with salt and a paper towel - and that should not be much needed.

Important Note: The reviews never tell you this but sauté pans with a slab of aluminum encapsulated in the bottom only will have serious hot spots all around the edges and stuff will brown quickly and easily burn there if you aren't careful. They are certainly usable and I used a 2 quart of that sort intensively for maybe 2 years, but the full laminate is better if you can afford it.

Critical Note: When selecting cooking vessels, always err on the large side. If it's a little too large, you can live with that, but too small makes proper cooking impossible.

. . and the first one anyone intending to fry should buy.

For covered work as you describe, I use a 10-1/4 inch 3" deep skillet similar to the Lodge L8DSK3 with cover L5IC3 except without the helper handle. Don't know who made it, it just says "Made in USA" (wherever the hell that is) and #7 10-1/4". I've had it for over 30 years and it was my primary cooking vessel for much of that time. Highly recommended for low cost cookware.