Farmer's markets are the way to go for produce if you have farms in your area. Some are overpriced and upscale, some are cheaper than your local chain grocery store. You can also buy grains/beans in bulk at lower prices, often direct from farmer's coops, and have it shipped to your door. Get a pressure cooker for beans, a rice cooker, save on the gas prices as they're electric, and use an induction electric stove. If you want meat, well, that's going to get more expensive. Eating less meat, but higher-quality, is going to be healthier anyway (boycott the factory farms, grass-fed beef is probably best).
However, you have to learn to cook. This is a barrier for some people. To me cooking is relaxing and I've got a lot of low-effort high-speed methods, but then I have a background as a wet lab researcher and that's about 100X as painstaking, where you're tracking every single thing you do in a lab notebook, mixing up solutions with precisely measured masses and volumes, adjusting pHs, running timers and working in this high-pressure environment where one screwup can waste a whole day's work if not a whole month's. Cooking in comparison, I don't use recipes, it's just pure fun. Get a decent collection of spices, that's important. Learn to clean as you go, and you can take most raw ingredients and go right to a great meal in half an hour.
If you've never done much cooking, a course isn't a bad idea. Indian cooking classes are great for teaching you how to cook a wide variety of grains/beans/veggies. Baking is more of a hassle as you have to measure stuff out and be more careful with temps and times, and tends to take a bit longer, but has the benefit of being able to make larger dishes for more people in one shot.