Preheat oven to 350.
Sautée onions in oil until translucent. Add grated vegetables and cook until soft. Press or strain any extra liquid out. Using a strainer over a plate and pressing with a spatula works well. Or, you can try to tilt the pan and mash the veggies with a spatula to drain the liquid. It's a little haphazard but involves fewer dirty dishes.
In a large mixing bowl, mix the cooked veggies and onions with the raw meat and seasoning. When the veggies are cooled enough not to cook the egg, add the eggs and mix everything thoroughly. I like to use my (clean) hands, god forbid. It's a tactile experience and hands really do seem to be the best tool for the job. You can't beat them, really.
Oil a loaf pan or glass baking dish (or line it with unbleached parchment paper). Transfer mixture into it's baking dish, pat it to make it nice and even, then spread the ketchup (or barbecue sauce) evenly over the top. Cook for 30-45 minutes, depending on depth of pan.
Deeper = cook longer. The old inserted knife coming out clean trick should tell you when it's done (well, except for the sauce on top) . The loaf also tend to pull away from the side of the pan and brown around the edges.
Variation: Bake in muffin tins to make little meatloaf muffins. These cook even faster. We actually like to use little silicone cupcake molds. Ah, meatloaf muffins! They're so cute!