I love cooking in cast iron, nothing beats the even sear you get, but it's quite specific in its use (not an "everything" pan) and requires upkeep to keep it seasoned and free of rust.
SS all the way. I keep two cast iron pans, one big, one small, and everything else stainless (except a non-stick for eggs as you mentioned). Any decent SS pan can last you a long while if you take good care of it. Get some Barkeeper's Friend to clean off the oil splatter that is going to burn onto the raised side of the pan and just to keep it looking new. Get a pan with a copper or aluminum layer sandwiched between the stainless pan and the stainless base. You'll get more even heat distribution, and avoid the odd hot-spots if you are cooking on gas.
Prices are all over the place. I have Cuisinart set and a couple of All-Clad pans that were passed down to me. You can feel the quality in the All-Clad (heavy as he) and it has fantastics heat distribution on gas. But the Cuisinart set is great too, and much cheaper; had it for about 7 years, and all are still in great shape with daily use.
If you're just going for one pan, I'd go saute over skillet. You'll appreciate having the higher sides.
Something like this.
https://www.amazon.com/dp/B00008CM6B/ref=cm_sw_r_cp_apa_glt_fabc_10G3NPQ20F5ZNMR8AEH7
IMO if it is going to be your only pan for a bit I'd go with a stainless sauté pan. I've had this Cuisinart one for the last 15 years or so and it still looks the same as it did the day I bought it.
The reason I suggest stainless, and a sauté pan, is versatility for a one pan house. I made chorizo and eggs in mine this morning. I can also boil water for pasta, heat tomato sauce, cook whatever. No worry about seasoning. It's also hard to do soup/liquids in a skillet.
That Cuisinart is $60, you can find a similar pan for less if you need too!
I do it all in the same pan, super simple. This is the pan I use and this recipe nearly fills it but never overflows. I like the shallower pan because it’s easier to brown and stir in than the big stock pots.
My boyfriend recently bought me a 5-quart stainless Cuisinart saute pan. This one to be precise. It is pretty large for my tiny kitchen, but it is a fantastic pan! I've used it a few times so far, making butter chicken, chicken parm, and sauteing various veggies in it. It heats evenly and holds it nicely. It's not too heavy, but definitely has some weight on it because of the thickness of the bottom, which is what you want. I went with stainless because unless you're only working with eggs or fish, non-stick is just not as good and doesn't produce the goodies that stainless does. It also comes with a lid (plus!), and the edge of the pan is a little sharper than you'd like to run your fingers along, but it's effective when you're pouring anything out of it, no drips! All in all, I like it a lot and would pick it again.