What is is the best cut to use for .....................?
As a butcher this is probably the question which I was asked most frequently. In the case of a beef curry where the meat is going to be cooked (stewed) for quite while, the cheaper cuts such as chuck (shoulder) steak, gravy (shin) beef, neck or cheek will give you the best results. These cuts are from the forequarter (front end) and are the right texture to be cooked this way. In addition, particularly with gravy beef, the thin layers of gelatinous tissue will dissolve into the sauce and give a nice rich texture.
NEVER be tempted into thinking that if the cut is dearer then it will make a better stew. Hindquarter cuts such as topside, silverside, rump, porterhouse (sirloin) and fillet are the wrong texture for stewing and will result in dry unappetising lumps of meat floating in a sauce. Either that or it will break down completely and produce a squishy mess.
The same basic principle applies to lamb and pork although not to such a great extent. The forequater meat such as shoulder and neck are more suited to long slow cooking but butchers often sell diced lamb or pork, which may well be a bit of a mixture of different cuts, but will usually give satisfactory results. My particular favourite in pork is the belly, better known these days as pork ribs. This usually has a higher fat content which adds to its succulence. If the fat is bothersome to you, cook it the day before and allow to go cold and skim the fat off the top before re-heating.
Chicken is easy, any part will do, although I prefer the leg and thigh, again because they tend to be juicier, but breast fillets will do fine. Just take care not to cook them for too long. (See Curry Basics)