Been a long long time since I last cooked some to be honest. I'd say use the fat or oil of your choice. Unsure about time, I used to judge it by eye. About ten minutes ? Yes shove loads of onions in, that is vital. One doesn;t simmer in oil/fat does one ? Give it a good fry.
Apart from the obvious (it comes from different animals) not a great deal I suspect. I used to buy lamb's normally but you can get calves, pigs, ox, chickens, etc.. I suggest you give them all a try and develop a preference, but unless someone here says differently I suspect it is probably subtle.