If I want to simmer or braise a piece of beef for a few hours, how do I choose suitable meat? Which of the usual cuts are great, which are adequate, and which ones will just turn tough? It would be great if you could, beside giving a list of the good cuts, also give some advice on visually recognizing the good meat, in case I am faced with a supermarket selection with no labels (or misleading labels) and no qualified personnel.
Beef for Slow cooking methods:
When shopping for beef that will be cooked long and slow, price per pound within a grade will be a helpful guide. Less tender cuts that will be best cooked long with liquid will be much less expensive than the naturally tender cuts that require less cooking i.e. filet mignon.
To visually find the right cuts of beef for slow cooking look for:
For simmering and braising it's good to choose a working cut, that is from a load-bearing part of the animal, as this will have connective tissue which will break down into gelatin as it is cooked. These make terrible roasts but great braises and stews. The other consideration is fat content - you have to remember in a braise or stew the fat isn't going to be able to drip out, so if you have a fatty piece of meat you could end up with a greasy dish.
In the past I've gotten very good results from shin (leg, foreleg), brisket, flank, and silverside (round). Parts from the neck and shoulder I personally avoid as they often have lots of gristle and fat, making it work to get at the good meat. A decently butchered pot roast would do though.
One thing to remember is to get a good quality meat. In the US most of what you find in the stores is Select grade, which has a huge range in quality, so look for good color with decent marbling. You are getting a tough cut, so when touching don't expect much give. In fact, if you get lots of give with a working cut don't buy it - it's probably old.
Short answer: Buy a cheap hunk of beef that looks like it has characteristics you like (e.g., lots of fat vs. little fat). Cook slowly. Enjoy.
I don't think there's a single answer to this question. It all depends on the texture, flavor, and amount of fat you want, as well as what you're willing to pay. The last consideration of cost is generally the driving factor for most people when slow-cooking. Slow-cooking methods like braising are typically used for cheaper tougher cuts.
Basically, most people tend to like tender meat, and there's no way to make chuck or round (for example) very tender without prolonged cooking. So we tend to use slow (and often moist) methods. But the reverse isn't true for tender cuts: you could cook a tenderloin or a rib roast and braise them like a pot roast. But there's little reason to, since you can find cheaper cuts that have similar textures and flavors. (That said, I have had a long-cooked braised ribeye once, and it was one of the best "pot roast" type meats I've ever eaten.)
From my perspective, any cut of beef is theoretically "suitable" for slow cooking. Braising, like long pit-roasting, is a "catch-all" cooking method that will work for just about anything. All meat will eventually break down and soften if cooked long enough. Many people tend to like meats that have a lot of collagen, fat, and other connective tissue to break down -- such as chuck, short ribs, or even less common cuts like oxtail. These end up with a significant "succulent" texture after the beef breaks down, which many people find desirable.
On the other hand, I know people who find cuts like chuck to be way too fatty for their taste. They're perfectly content with a leaner cut from the round, for example, to make a leaner pot roast, usually served with flavorful gravy or sauce. It's all a matter of preference.
Some people like the strong "beefy" flavor that can come from bony areas like a shank (sometimes seen as a shin or leg cut) or oxtail, or even more "variety meat" elements like tongue or heart. These are all great candidates for slow-cooking methods, if you want that much flavor. Others prefer milder cuts.
Now, you could use ribeye instead of chuck for a fatty result, or use sirloin or even filet mignon instead of round for a lean result, and end up with a similar end-product. But why would you spend the money? (Actually, there is a bit of a disadvantage to using tenderloin/filet, since it doesn't have as much flavor as lean tougher cuts like round. But there's no reason you couldn't braise a tenderloin for several hours; some people may actually prefer milder flavors. Everyone has their own preferences.)
The one advantage to using a tender cut for slow cooking is that it will soften again faster. Where a chuck roast might need 6-8 hours (or more) in a slow cooker to become tender, a rib roast might be fork tender in half that time or less. But that's usually a high price to pay for a quicker pot roast. And many people would prefer to make rarer "prime rib" or steaks instead with that cut.
If you are in the US and are looking at graded meat, it's also important to take into account that the USDA grading system is designed to tell which carcasses produce the most tender steaks. For most meat you see a grocery store, grading will only represent degree of marbling (which adds both tenderness and flavor when cooking fast). The grading is NOT designed for evaluating tougher cuts that will be cooked for long periods. Someone in my family was once convinced at a high-end butcher shop to buy a "Prime" chuck roast at close to three times the cost of a "normal" chuck roast. The quantity of fat within this roast was incredible. It was bought to become a pot roast, and after many hours in a slow-cooker, it had shrunk to less than 1/3 of its original size, sitting in a giant pool of liquid fat. (In fact, there was so much fat left that I siphoned it off and used it for multiple batches of tortillas.)
Bottom line: the USDA grading system tells you nothing about "quality" for a slow-cooker. Again, most people use slow cooking methods to cook cheap cuts, and lower grades are often fine for this purpose.