Right now we buy Classico. But I am curious - is there a way to make
homemade pasta sauce that is better than premade jarred namebrand?

I'll throw mine in. If you want quick, use one big can of crushed
tomatoes and one big can of concentrated crushed tomatoes. The
concentrated is thicker, and the sauce doesn't need to cook down as
long.

Throw in some red wine and chicken broth, maybe 1/4 of each.

Season with S&P, Italian seasoning, and simmer for a while.

I usually sautee onion, green pepper, and garlic in the pan before
adding everything else.

I usally make sauce from my canned garden tomatoes, but whe those run
out for the year, this is how I make my sauce.