I always make my spaghetti sauce with fresh tomatoes---I never really noticed a grainy texture, more of a chunky/hearty texture, which is what I prefer. If you would like a smoother texture, you can blend it after it is finished. I live in Italy and this is my amazing, foolproof spaghetti sauce. Italians as a general rule do not put meat in their pasta sauces, but traditional American spaghetti sauce does exist in one city---Balogna. It is referred to as Balognese sauce here

So anyhow, this recipe doesn't include meat, but if you want it, just add 1 lb. ground beef to the onion sauteing step.
1 large onion, chopped
6 cloves garlic, minced
3 big mushrooms, chopped
5 tbsp. olive oil, divided
1/2 cup red wine, divided
1/2-1 red bell pepper, chopped
lots of chopped fresh tomatoes (at least 6 cups, after chopping)
1, 4-6 oz. can tomato paste
3 tbsp. fresh basil, chopped (or 1 heaping tbsp. dried)
2 tsp. dried oregano
1 tbsp. salt
1 tsp. pepper
2 tbsp. dried parsley
Saute the onion, garlic, and mushrooms in 2 tbsp. olive oil until nice and soft, about 10 minutes. Add 1/4 cup red wine and the bell peppers and let simmer uncovered for 5 minutes or so, allowing the mushrooms to soak up the wine. Dump in the tomatoes, the tomato paste, and the spices. Increase heat to medium-high and gently boil uncovered for 30-45 minutes. Reduce heat to low, add remaining wine and olive oil, and cover pot. Allow to simmer for another 30 minutes or so, until you get the thickness you prefer in your sauce. Taste sauce and adjust seasonings to your liking. This recipe made with meat will cover about 4 very hearty adult plates of pasta (main dish with a salad). Or if you leave out the meat, it will serve about 8 as a first course with a meat dish following.