The trick with eating budget as a singleton is that unless you want to skip fresh fruits/veggies altogether, you have to pony up a bit of extra cash to buy those in small portions to prevent waste. That price per lb. can be hard to swallow if you're trying to cut costs.
This is why I used to make it a point to average my price per meal over a week. Some days when I went heavy on the fresh items it cost a bit more, but other days when I used my stock of frozen &/or dried items I balanced that out.
One-dish meals and soups are going to be your least expensive overall, so you do need to mix a fair number of those in if you are trying to cut costs.
Freezing your own veggies works quite well for those that can be frozen; you don't have to go with factory-frozen, and veggies are cheapest at your farmer's market. Just get yourself some good containers to freeze them in. I keep a selection of fresh-frozen mirepoix in my freezer for dishes that require it, along with things like frozen sweet pepper strips for sautes. Not as good as fresh, but not bad, either as long as the dish does not need the crunch. Fresh cob corn freezes fine; just clean it and cut the cobs in half so that they will fit well in bags. If freezing small veggies or veggie pieces, freeze them on a cookie sheet covered with foil first, then slide them off the pan and into a baggie. (Using a bit of oil or a piece of parchment makes that easier.) Celery seed adds the flavor without the spoilage issues, but you can certainly freeze chopped celery.
A word about mushrooms: they don't freeze well unless they are cooked and in a broth/sauce of some kind. If you want to keep some around without waste, use mostly dried. They are easy to find at Asian markets. I reconstitute them in a bit of wine before cooking.