In our house bolognese sauce is usually referred to as Sugo - that's the Italian word for any sauce like this. It's also referred to as meat ragu, but the bottom line is that most of the time the sauces have more in common than they do differences. Mine is quite simple really - I always use onion, carrot, celery, beef, tomatoes, wine and herbs. Sometimes other things get added, and I might use different herbs and wines (even white wine sometimes, which is surprisingly common in Italy), but it's the beef that really makes the sauce.
Sugo in progress, with roast cherry tomatoes (and a solitary half pepper in the middle!) that I was doing at the same time
Since I discovered how fab Rib of beef is (on the bone, naturally) I always buy it if I can get it. But it's not cheap - you can easily set yourself back £30 or so for a large joint. But I maintain that it's actually one of the best cuts for thrifty cooking too, because at the end of the day you can get so many meals out of it that it starts to work out at way less than £1 per meal. I even did some calcuations the other day to prove my point, and worked out that a piece of Brisket that I bought the other day actually worked out more expensive than Rib if you consider how many meals you can get out of it! Of course there are wonderful things like beef sandwiches made with the rare eye form the middle, curry made with slow cooked chunks from the top and the bits from between the ribs, broth made from the ribs themselves gently simmered with whatever other flavours you fancy, and maybe a few bits of pasta dropped in for good measure, but for me the very best way of using it up is to make lots and lots of really good sugo.
Now the recipe bit. The trick with the left over beef is to mince it coarsely, and then to fry it hard in a little of the left over beef fat until it's almost getting crispy. Make sure at this point you don't overfill the pan and do it in batches if necessary. What happens is you create a wonderful texture in the meat. You might think it dries it out, but the next stage (after lightly frying the onions, celery and carrots separately and adding them in) where you add lots and lots of tinnned tomatoes, wine and herbs and then simmer for at least one and half hours (prefereably longer depending on quantity) gives the meat back it's tenderness, and gives a wonderful texture as well as rich dark flavour to the sugo. I always pot it up once it's cooled, and the freezer becomes a life saver after a long day in the office when you can just defrost a pot of sugo for two and be eating incredibly good bolognese in half an hour. Now that's my idea of an instant meal!