Chuck is likely the most common cut of beef most people have without knowing it. Chuck has a really rich flavor, and a fairly balanced amount of fat. While chuck is cut as steak sometimes, its most commonly consumed as ground beef or as a pot roast (image to the left). For this reason, best way of cooking non-ground chuck is by roasting in a pot, slow cooking, or braising it. If you want to eat beef on an affordable budget, look no further.
Flank is another cut that is best suited for braising and cooking slowly. Due to its high fat content, slow cooking this cut is key in order to get a quality cooked steak. If you've ever had fajitas, you've most likely had flank steak.
Short loin is the cut of choice if you want beautiful grilled steak, and probably my favorite. This cut is one of the most tender cuts with a rich beef flavor. Famous steaks from the short loin are porterhouse, Kansas or the heavenly New York Strip, tenderloin and fillet mignon.
Sirloin is similar to the short loin cut, normally with a higher fat content. This is the cut that I most commonly buy, because of its rather high quality for a much cheaper price than short loin. When looking for sirloin in the store, aim for top sirloin, as its the highly quality sirloin cut. Pretty much any preparation can be used on sirloin, aside from slow cooking methods.
I hope this is helpful, and comment if you want any other food guides!