One of the most important things is a full tang. The tang is an extension of the metal of the blade into the handle. In knives with a full tang, it goes all the way through the handle. This improves stability, control, and durability. Cheaper knives with partial tangs will have the handle break off over time.
In a chef's knife, you want a blade from 8 to 10 inches long, whichever is more comfortable.
You can also either get a forged or stamped blade. I suggest reading this article on the differences. To summarize, forged blades are softer, easier to sharpen, heavier, and have a bolster. Stamped blades are sharper, harder to sharpen, lighter, and have a welded on a bolster if any. With current manufacturing processes forged is not necessarily better than stamped. You should make your own decisions. All crap knives are stamped, but not all stamped knives are crap.
This brings me to one of the most important points: It must feel good in your hand. Don't buy an expensive knife just because it's expensive, or you recognize the name. Go to a store that will let you use the knife, Williams-Sonoma will do this. If you can, bring a carrot in your pocket and actually cut that in the store.
I'll do some research on steel quality and update this later.
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.
Best Answer
Ceramic does not quite have the nonstick properties of "true" (based on some kind of PTFE-ish material) nonstick, neither does enamel. Especially not for applications like jam making where charred jam might get stuck to the bottom. Also, from my anecdotal evidence, ceramic coatings hate thermal shock (eg when adding cold liquid into a hot pot to deglaze) and can stain.
The damage shown in the photo does not look like normal wear, but like wear from using tools that aren't inherently nonstick-safe too forcefully - metal-based immersion blenders, metal wire whisks, metal spoons....
But then, wear of "true" nonstick surfaces happens - slower if treated gently, faster if treated rough, so eventually, non-stick cookware that is seeing regular use will need to be replaced.