I think one good mindset for this is to recognize you don't shop by what you want to eat, you shop by what's on sale, period.
If I want chicken breast, which is $3/#, but thighs are $1/#, I buy thighs. We know we want to eat plenty of fresh fruit, so I check the ads and often decide which store to shop at based on the sales. For example, this week we're eating watermelon because it's 25¢/#. I don't buy organic milk for the college aged kid who goes through 1-2 gallons per week
You also have to know the basic good values in food. Cabbage, carrots, onions, and potatoes are always a good value. Other produce has a price cycle related to seasonality. Apples go low priced in the fall and winter, as do Brussels sprouts and broccoli. By next month cantaloupe will be $1 each, and grapes hit that price in late summer.
The grocery bills get cheaper the more you eliminate highly processed foods, convenience foods, prepared foods, and junk foods. This makes room in the budget for high quality foods. I buy organic cream so I can get it with zero additives. I buy grass-fed and finished ground beef, but go conventional for steak. I don't worry so much about chicken, as organic operations really just come down to the feed, since "access to the outside" doesn't mean they get to go out.
Knowing how to make food is a good money saver. We eat almost no processed food (other than it being minimally processed, such as beef being cut from the carcass, oil being pressed from olives, cheese, etc.). One thing the pandemic showed us was how much we hate processed convenience foods -- not the college kids, but DH and I. Now we base our meals off meat and produce, with produce being the major portion of our diet. We don't spend money on desserts or sweet foods -- fruit becomes incredibly sweet and valued when you give up added sugars. We mostly don't eat grains, but if we want bread, I grind wheat and make sourdough bread. If we want polenta, I grind corn. If we want soup, I make stock. I culture yogurt and creme fraiche. I grind almonds into almond butter in the food processor. I make ghee. Now these things can be time consuming, so I don't do them all the time. I don't bake bread in summer because it heats up the house.
Simple is easier and cheaper. We eat the same dish for more than one meal. We use leftovers in new dishes. We know our favorites and mostly eat those meals, adding in enough variety to not get bored (soon we'll trying a savory cornmeal waffle recipe).
We don't buy organic everything. We don't even buy everything on the dirty dozen list organic, because quality also matters and often the organics we encounter are old and deteriorating. We instead focus on local produce plus loss leader produce (usually very fresh). A diet of fresh meats and fresh produce is going to be healthier than one full of organic processed foods. As for meats, I think with fresh meats the pasture vs. conventional questions is mostly about the animal treatment than the nutritional makeup of the meat. People write a lot of books and articles full of opinions about meat and other foods that aren't entirely true. For example, I can't tell you how many times I've read that ultra pasteurized dairy is dead and won't culture -- it cultures just fine and saves the step of heating and cooling the milk. Grass-fed and finished beef has a lower fat content, but low fat diets have been debunked. It also tests higher in omega 3 fatty acids, but probably not enough to justify calling conventional meat unhealthy. For us I definitely consider this a choice not made for health reasons.
Mostly, we understand that healthy eating really comes down to eating a produce forward diet of unprocessed and minimally processed foods. There are no super foods, just the current marketing darlings. There is no miracle diet (paleo, vegan, keto, etc.) just the reality that human bodies need protein, fat, carbs, and fiber, can't process too much glucose at once, and need a variety of micronutrients which can be found in food.