Careful with tomato paste, if you're a rookie. It must be cooked down to elimante the raw canned taste. Put it in a sauté pan over medium/med-low heat for a couple of minutes. Or start with the paste for your sauce in a larger pot and cook it first and and add some spices to the paste (dried, I assume, if you're limited on ingredients--oregano, basil, garlic or even onion powder...) then add the sauce and simmer.
I've used a recipe for bolognese that used milk (pioneer woman), so you could try adding that. If you have fresh onion and some carrots, you can throw them in the food processor and cook until soft before adding the other stuff.