I often shop just the opposite of planning a menu and then buying the ingredients. I will go to the store in the evening, and look at what food has been marked down and build a meal around that. There will be bread that didn't sell that day, lots of items on the clearance rack (most large grocery stores have a clearance rack, usually way back in the back of the store, sometimes partially hidden), half-price dairy on the bottom shelf of the dairy case, and meat bargains! Most grocery stores have a section of both the meat and poultry cases that are called something like "manager's specials", and they'll be 50% off or more. Get to know your store, and ask the manager when and where these bargains can be found. I asked the meat guy and he said 6 pm every evening is when he starts marking meat down. And I bargain! Once there was a leg of lamb, after a big holiday. It was the last one, and was something like a ridiculous $30. It was marked down to $15 and the meat guy was moving it around, looking for a place to put it. I boldly said "I'll buy that and get it out of your way if you can mark it down even further". He looked at me, took his Sharpie and made it another 50% off! I made so many meals out of that! Be friendly and polite and let them know you're a steady customer and you never know what they'll do!
Often I am not sure what to do with a particular cut of meat, but by googling it I can find ways to cook it and use it. Or if I come home with a weird assortment of bargain foods, just type them all into google and a lot of recipe ideas will come up! If it's a $1.50 marked down from $7 but I've never heard of it, who cares? Somebody somewhere knows what to do with it, and it's on the internet! Be brave!
There is a great web site called www.lovefoodhatewaste.com and if you click on the "recipes" tab on the right, you'll find a list of food. It's called "What needs using up?". At the bottom you can expand the list. If you find celery, for example, on sale and have a lot of it, that site will give you some ideas for using up that inexpensive celery. It is a British site, so some of the words are a little unfamiliar (and the money is shown in pounds), but the basic information is great.
And learning how to use the entire item is another great idea. A bargain brisket can be cut in half, with one half cooked in the crock pot with vegetables for a stew, then the stew can be thickened and made into pot pies, or mixed with rice and soy sauce for a beef rice dish, or Mexican seasonings for enchilada fillings. The other half can be ground up and made into burgers or meatballs which go on spaghetti and then can then be meatball subs. And the leftover burgers can be chopped up and mixed with tomato sauce. Just keep using one ingredient until it's gone, and has been turned into a multitude of dishes.
I think it's adventurous and I hope you have fun making your budget friendly foods into great meals!