I live in a house of 7 young adults and we average about $95 a month for food per person. It helps a lot that we eat vegetarian 90% of the time.
If you can get fruits and vegetables for less than a dollar a pound go for it.
I have found that in frugal grocery shopping, where is sometimes more important than when or what. For example, the dirty, smelly asian marts offer great price points (sometimes lower than 50%) compared to the brand name grocery stores. Also, near where I live, there is a speciality grocery that sells B grade produce. These are things that would normally not make it to the brand name stores shelves since they are bruised, oddly shaped, too old, etc, etc. Often they are marked down to less than 30% of their "normal" price. One time I got button mushrooms for 80 cents a pound, for example. Huge foodservice bags of Kale for a dollar a pound.
If you pay more than a dollar a pound for processed soy protien like tofu, TVP, etc, its probably a bit of a ripoff although to be honest I have yet to find cheap tempeh.
I try to avoid paying more than 1.25 a pound for tomatoes.
I buy cereal at about $2 a pound or less. oats and Malt-o-meal.
Squash should be less than a dollar a pound. Note that squash has about a year of shelf life so stock up when its on sale.
Catfish I can usually find for less than $4 or $5 a pound.
You can usually find peanuts for around 1.40$ a pound or less IIRC.
Sunflower seeds are another good and cheap source of protein, I don't remember the exact price though.
Things like spices, oils, sesame seeds, etc, are MUCH cheaper when you buy the huge container. I try to buy whole spices exclusively because they have a radically longer shelf life, so buying in bulk works better. A bit harder to cook with, but more fun in my opinion. We have a coffee grinder dedicated to spices.
Soymilk should be less than $5 a gallon.
Ask around and see if your locale has any stores that sell b-grade, or any large mexican, asian, etc grocery stores in the poorer part of town, they might have great prices and fun products you cant get anywhere else. If you can't find those your might be able to save a few bucks by visiting discounters like Aldi.
Please note that any prices that someone quotes you are going to be relative to the local shipping prices, taxes, seasonal, etc.