Need help choosing burner for wok

Make sure to seriously wash the wok before initial use. Scrub it with hot soapy water and dry thoroughly.

After drying, place the wok over the stove on high heat until it starts to smoke. Rotate the pan so that all parts of the inside are exposed to high heat. Then rub the wok with oil on a paper towel.

After this, try not to scrub the wok. A rinse and rub down are usually all that is needed to clean it up. Always rub the wok with a little bit of vegetable oil after washing/drying. That will help to prevent rust.

And the most important factor of seasoning a wok is to use it. It's definiteily my most used kitchen item, and it's just getting better and better with each use!

I'd say there are basically two material options. Plain (seasoned) cast iron or enameled cast iron. I prefer enameled, because you don't have to worry about keeping them seasoned--just wash as you would any other pot--and the enamel surface is easy to get clean. But they're also more expensive by a significant margin. A properly maintained plain cast iron one will be awesome too, and do everything enameled will do for less money, so don't rule it out.

What you should consider:

The foremost thing you want to look for is a heavy pot. Heavy bottom AND heavy sides and lid. You want something that holds a lot of heat when you need it to, and heavier often means more even heating and better searing (crucial for braises and pot roasts).

Consider the lid. It should fit well, without gaps or sliding around. Some have loop handles on the side or on the top, some have a knob on the top. All are fine, but keep in mind that a metal lid handle will be more durable with all the oven time your dutch oven will likely see. They say the plastic ones are OK (Le Creuset, a trusted brand, uses them so they can't be that bad) but I'm not 100% convinced. Whatever handle you get, think about how easy it'll be to grasp wearing an oven mitt.

Handles on the pot itself are a potential issue. Some plain cast iron pots will have a bucket-style bail handle, which I don't think is that great for the kitchen, especially the oven. These are really intended for campfires and camp stoves, so I'd avoid them. Sturdy, compact but easy-to-grip handles of any type are good. It'll be heavy, so make sure you feel secure holding on.

Size is another consideration, and it's a tough one because it's so individual. I think between 5.5 and 6.5 quarts is pretty standard and works for most cooks. A dutch oven isn't like a stock pot, where big is always good. You want one big enough to cook the things you want, but you don't want it to be too huge for what you have in there, or you'll give up a lot of cooking liquid to evaporation too fast. This is less crucial for soups and stews (I'd do soup in a regular stock pot), but for a braise it's kind of important. So I would resist going too small, but don't go too far, especially if you're always cooking for two people. Also, bigger = heavier, so don't let your eyes get bigger than your muscles!

Another option is shape, as they generally come in round or oval. Oval sometimes helps people who can't decide how big to go. With roasts being generally oblong, an oval pan can fit a proportionally larger roast without getting really huge. With a round pot, your whole pot needs to be at least as big around as your roast is long. Ovals are a little less common, however, and generally don't come as big as round ones. They're often more expensive too.

Finally, don't compromise too much on size or cost. Any halfway decent dutch oven, properly looked after, will last much longer than you will. Make sure you're getting what you want, because you'll be living with your decision a long time.