Congrats! Cozi has a free recipe/meal planner/shopping list website, and YNAB is good for budgeting. And most grocery stores post sales and coupons on their websites these days. Wegman's app/website is amazing if you have one nearby. But, trying to come up with complete optimized meal plans using coupons/websites and following a different recipe every night can be overwhelming when you are just starting out on your own. Maybe focus on one part to start, like which meat is on sale that week.
My advice: Try asking older relatives and friends (especially those whose cooking you really like) for one favorite cheap easy dinner idea that's easy to modify and ask them to teach you to make it. And I don't mean the complicated type that you find in cookbooks or have on holidays, I mean every day cooking that's easily modified to ingredients on hand. Like recipes for rice dishes, curries, veggie hash, ground meat, chicken, canned tuna, soup, etc. Collect ideas that sound good, and slowly build up your own 'cookbook' of fast easy meals with simple ingredient lists stored up in Cozi or Evernote or wherever.
Learn how to make a few of these really really well and memorize the basic pantry ingredients required. Stock those key ingredients when they go on sale or buy in bulk. Pick two or three a week that share similar ingredients, make a plan and shopping list from that (check your pantry first!), adding meat that is on sale and produce in season (or frozen in winter). Make lots, and you'll only have to cook a few times a week (make enough for lunch too). As you get better at cooking, add more recipes to your collection.
For example, tonight's dinner: rice with onion, garlic, red pepper, frozen peas and carrots, chickpeas, and one chicken sausage cut into pieces. 1 pot. Now I have enough rice for tomorrow's lunch and dinner, plus I didn't even use up any of the above ingredients so they can be used in Saturday's dinner and beyond. And it could have easily been any number of other combinations of bean, vegetable, and meat.