Eating cheap for a single person
Most cookbooks and cooking shows assume you are feeding multiple people. For those of us that have been single for many years, this just isn't true.
To keep food fresh, minimize the amount of surface area exposed. For cheese and vegetables, you may be able to cut off the surface layer that has gone bad and use the rest. Lettuce should be used from the outer leaves in, throwing away the wilted outermost layer if needed. A head of lettuce can last 3 weeks this way. To get diced onion, cut a slice or two, then make a series of parallel cuts one way and another set at a 90 degree angle.
Some kinds of food (like milk) I won't eat much after the expired date, and others like pasta in sealed packages are just fine years later, other than being less flavorful. Canned food is usually among the latter, but bulged cans should be discarded. Acidic foods, such as pineapple and tomato sauce, can react with the metal in the cans and shouldn't be eaten if the smell is off. Some foods like produce keep longer if kept cold, and others like pasta and chips better if they are kept dry. You'll need to decide if it is worth your limited refrigerator space to keep things like potatoes. Multiple small sealed packages may be the best value for a single person, even if the per-ounce price is much more.
The major chain stores tend to have better weekly specials, but are more expensive than the discount stores on most everything else. Produce tends to be cheaper where Mexicans shop, but the quality needs to be watched closely. Mexican pasta comes in small packages and is cheaper per pound than the US or European pasta. I've seen stores take meat out of "expired" packages and put it to be sold at their butcher counter.
Dollar store food tends to be about to expire or actually expired unless it is something regularly carried, and sometimes is more expensive than other stores. Milk, which I only use for cooking, comes in quart containers and tends to be fresher than the small containers in supermarkets. (A quart is about the amount of milk I use in 2 weeks, about as far forward dated as I can find.)
Marked down, about to expire, foods can be quite cheap -- or very overpriced. Mark-down racks tend to be located in the back of the store, sometimes partly down an employee hallway. Whether they exist at all, and how deep the discount, can vary store to store, as well as between chains. I've seen stores mark down something from regular price, and have the exact same item with a much later expiration date on special for cheaper elsewhere in the store. Consider if you will consume it before it goes bad, and price compare to the item you would normally consume (where you would normally buy it) rather than the regular price of the deluxe item being discounted. Pre-grated or sliced items may save in prep time, but tend to spoil faster.
When comparing prices, include your time and gas money. It doesn't make sense to spend an hour and $3 in gas to save $.50 on a few items.