I am interested in getting some form of cookware that will... take seasoning? Become seasoned? Cast-iron, carbon-steel, et cetera. I currently have two pots (one tall, one short) and one nonstick stainless-and-aluminum pan. I do not have infinite money or shelves so I do not want to buy all possible cookware. I am also uncertain whether a pan or a wok would be preferable.
For any pairing of (carbon steel, cast-iron, forged iron) and (wok, pan), what would be preferred?
I think any of the suggestions you made are great. I would add, what type of food/style are you cooking or interested in? More into the stir-frying, than a wok would be a good choice, besides they are quite multi-functional (fryer, steamer, stir fry, smoker). They are also pretty inexpensive when made out of thin carbon steel.
If you are not into that, then a cast iron or my favorite are carbon steel pans. Nearly all the seasonability of cast iron without the weight. The carbon steel is usually also much less expensive. Lodge makes a set of carbon steel pans. But most carbon steel pans use rivets to secure the handles to the pan.
If you are getting fancy, there is a German brand of carbon steel pans, which makes them out of one piece like a cast iron, no rivets. The brand is named, Turk, Albert Turk GmbH.
Good luck.
Your stove is a significant factor in whether a wok is worthwhile versus a flat bottomed pan.
Woks benefit from very high heat. Some people think you need a professional stove to use a wok properly because a residential stove heat output is too low. There is a characteristic wok hei flavor that is a result of using this heat that probably is not reproducible with a residential stove.
A wok does not have the heat capacity of a cast iron pan because it is relatively thin. You can preheat a cast iron pan for awhile before cooking to sear, but this does not work with a wok. You need to continuously apply high heat to sear in a wok.
With an electric stove, I prefer to stir fry in a cast iron pan over a wok, while over natural gas, I prefer to stir fry in a wok. Over an electric stove, you need to divide the cooking into small batches to prevent your stir fry from becoming a simmer/boiling. I have no firsthand experience with induction stoves, but I have heard they are better than electric for use with woks.
To summarize, if you have a high heat stove, consider a wok. Otherwise get a pan.
I would choose cast iron and pan, but I don't know that my preferences have much to do with what you should buy. I have a steel wok - can't recall the last time I used it; I last used the cast iron pan, day before yesterday. I've never really "gotten into" wok-ing, so my results tend to be better with other methods. For other people with other cooking habits, that will be different, as seen in the "related" questions off to the side.
I'd recommend a Lodge Cast Iron Skillet (12" or 15 1/4") and a Lodge Cast Iron Wok.
Both options are fantastic values, will last literally forever, and are a joy to cook with.
