I use 5% fat minced beef, browned with soffrito and garlic (lots). Chuck in lots of puree, two tins of chopped plum tomatoes, two oxo cubes, some frozen italian herbs, a dash of worcestershire sauce, a dash of nam pla sauce (which sounds crazy but really really does work) and a good glug of red wine. Reduce it all down for a good 20/30 minutes. I always put grated courgette and carrot in, plus chopped peppers/mushrooms, but appreciate that it's a question of choice and to be honest it's more about using up leftover veg than intrinsic to the recipe.
Make your own béchamel sauce - it's melted butter in a pan, once it's melted mix in a few spoonfuls of plain flour (off the hob) and keep mixing til it makes a thick sort of paste. Add milk - a little at a time - and put the pan back on the hob. Whisk the mixture constantly and continue adding splashes of milk til you have a proper thick sauce.
I add grated cheese to my béchamel, then layer it up with mince at the bottom, lasagne sheet, mince again, lasagne, béchamel, lasagne, mince, lasagne, béchamel and finally I grate more cheese for the top, then add chunks of mozzarella and fresh basil leaves, bake it for 35/45 minutes and serve with garlic focaccia and a salad.