L.R.
I think I might be able to help. Maybe.
You're probably not vegetarian. I am. If you aren't, I can't give you any advice in that department. But for the rest of it, maybe you might find some helpful ideas.
First off, buy at Winco. They are the cheapest place around, for the most part. You can stock up on bulk items like oatmeal for 43 cents a pound, pasta in bulk (even whole wheat pasta), and they even sell a few organic things (carrots, for instance). I don't buy much organic myself, because I can't afford it. Maybe if I didn't have to buy hemp milk for my son to drink (he's allergic to dairy and soy), I could afford more organic produce.... Buy beans. You can cook a lot in a crock pot overnight, then freeze meal-sized portions for use later. Beans are cheap, especially dry. I can my own beans, and I figure that for the price of 3-4 cans of beans, I can get 7 quarts. That's a lot of savings! I usually stock up on bulk items at the beginning of the month. That way we will have food, even if we run low on money by the end of the month. It's easier to limit fruit that is more expensive than it is to limit the things that you fill up on.
Try experimenting with making more from scratch. Once you're home more, you should be able to make a lot more from scratch. That way you can make lunches to take to work and save on take-out. Get a bread machine (you can usually find them at the Goodwill) and make your own bread. You can put all the ingredients in before you go to work and set it with a timer to start so that it finishes just as you get home. There's nothing better than home-cooked bread, and it costs less than $1 a loaf. Plus there are no preservatives in it. You can find good bread machine recipes online. Don't use the premixes--they are as expensive as buying ready-made bread! Depending on how much bread you use, this can definitely be helpful. We don't use a lot, but we still make our own bread (my husband is from a country where only rich people eat bread, so we don't eat it at every meal like many Americans do).
You've probably heard this before, but make a menu. Then build your shopping list around the menu. You can make your menu based on the sale items in the list. For instance, planning a dish with broccoli in it wouldn't be such a good idea when broccoli is $1.50 a pound, but would be better when it's $.88 a pound. Closely monitor what you have, so that you you don't waste food, also. Buying 5 heads of broccoli because it's on sale is only a good idea if you're making a broccoli dish to take to a potluck--or unless you have 10 kids. Just buy what you know you will use within a week or less.
Check the dollar store. I know Dollar Tree sells frozen strawberries, peaches, peas, corn, and mixed vegetables (at least, the one near us does), for $1, and ounce per ounce it does come out a bit cheaper than WinCo most of the time. But you have to be careful. Sometimes they can be a cent or two more expensive (to make that even $1). They also have other stuff cheap sometimes, too. You just have to know what things are worth at your regular grocery store.
Consider using homemade rice milk as an alternative to cow's milk sometimes. Especially in recipes. The recipe I use goes as follows:
1/2 cup long grain brown rice (about $.55 cents a pound at WinCo)
4 cups of water
1/2 tsp salt
Bring to a boil, reduce to low, and simmer for 3 hours.
Then take equal parts of this soupy rice mixture and water and blend and strain (don't use a cheesecloth; just any scrap of calico-like cotton fabric will work fine). Sweeten and flavor as desired (I leave it unsweetened and sweeten it as needed). This tastes almost exactly like Rice Dream, and only costs pennies per quart (this recipe makes about 2 quarts). This is cheaper than any other milk available, hands down.
I make my own soy milk, also. I bought a soy milk machine, because it was a lot of work to make by hand. Then I buy organic soybeans and make milk for about $.25 a quart, and tofu for about $.75 a pound. As vegetarians, this really is a savings. I just have to buy the soybeans ahead of time, in bulk, because I want them organic.
Other than that, try to avoid having a lot of exotic foods. Once in a while a fancy meal is good, but usually we have the same thing on the same day of the week. For instance, this morning we had plantain bananas (not super cheap, but a favorite in our family--cost about the same as sweet potatoes) and black beans (home-canned, therefore super cheap). We almost always have them on Tuesdays, unless we are out or they aren't ripe enough. Sundays we usually have waffles. I make them up in bulk and then we can wake up whenever we want and all we have to do for breakfast is to warm them up and top them. Which reminds me, get peanut butter in the bulk section at WinCo. It's about $1.43 a pound, which is considerably cheaper than what you get in the largest size on the shelf, and you can buy in small batches to keep it fresh longer. It's got no sugar, either.
Also, I would avoid any of the toddler foods. At 2 years old, your daughter should be able to eat just about everything you eat--that is, if she will. If not, you can always have cheap, simple things on hand that she likes, like pasta.
One thing we do is have a grocery budget. Thanks to my son's allergies, it is sometimes hard to keep in budget. I went $7 over in March. I used my own money to make it up, rather than asking my husband for more (I don't work outside the home, but bring in a little in sewing jobs). If I hadn't spent $27 on a case of hemp milk (on sale), I would have had an extra $20. But then I would have spent that in about 3 weeks on buying it for $4 a quart at Fred Meyer, and would have gone more over the budget than I did. If he wasn't allergic to so many things, he'd still be nursing and I wouldn't have had to buy it at all. But that's what we have to deal with. Plus, if I hadn't bought those pears that turned out bad and had to be thrown out, I probably would have about broken even. That's how it goes.
They say that a reasonable budget for a family is $100 per person per month. We have 2 adults, a 3 1/2 year old, and a 14-month old with allergies, and we spend about $330-350 a month. If I clipped coupons, maybe I could save more, but it's so much work and there's so few coupons I would actually use anyway. Plus, who wants to go to more than one place to shop when you have two little ones to take in and out of their car seats?
Hopefully that will give you some ideas. :)