I am following this recpie to make a lasagna (minus the ragu because jewish law) and I always wonder how to best layer the lasagna.
Traditionally, you start with a layer of pasta at the bottom, then go ragu-bechamel-lasagne-ragu-bechamel-lasagne, and finish with a layer of bechamel directly on top of the last pasta layer, followed by a liberal covering of grated parmesan.
It is also common to add a sprinkling of parmesan on top of the bechamel in each layer.
Ratios are subjective but I would say it is normal to have roughly twice as much ragu as bechamel
There are probably as many variations as there are people making it. It's probably a good idea to spread the ragu/red sauce a bit more evenly (I usually use a vegetarian ragu with lentils instead of the meat)
I tend to make mine ragu/pasta/bechamel/pasta/ragu/pasta/bechamel/cheese but regard that as a matter of preference. I think this approach is common in France, which almost certainly means it's not authentically Italian. Actually, there's some cheese added to the bechamel in my version. I also use the type of lasagne that doesn't need precooking, which absorbs a bit more water from the sauces and thickens everything
I find it better to have the pasta slightly underfill the dish than end up trying to tessellate fiddly bits.
But this is all a matter of preference.