One reassuring thing to know is that frozen vegetables are more nutritious than "fresh" ones that were actually picked a week ago and shipped cross-continent. That's because the frozen ones get packed right away w/vitamins intact. The same is true of canned food, but it often has added sugar and salt which decreases the healthiness.
Look for big packages of healthy foods; they're usually a better deal, but check price-per-ounce (many stores put it on the shelf tag) to make sure. When you get it home, divide it among several resealable containers so that you have one to use and one or more to put away for later. Try to find a space in your home where you can store extra food and won't lose track of what you have. That way you'll have enough space to stock up when there's a good price.
If you can find time to cook dried beans (they don't take a lot of attention; you just have to be willing to stay home for a couple of hours to keep an eye on them) they are really cheap and a great healthy protein source. Even canned beans are pretty cheap--50c buys two meals' worth. Rinse cooked or fresh-from-the-can beans to remove the gas-causing stuff.
Look for a co-op or health-food store where you can buy things in bulk using your own container. That often saves money, esp. on organic or all-natural things. Also, look for stores that sell surplus from the big chain supermarkets; often it's stuff w/packaging slightly damaged so that it looks less-than-perfect but isn't damaged at all, and you can find some amazing bargains! (To those in Pittsburgh, I recommend KML at 16th & Smallman!)
Lots of vegs and fruits freeze well, so you can buy them on sale and freeze for later. I'm sure there are detailed instructions about this somewhere, but I've had good success w/2 basic principles: Get the air out (put in a zippered plastic bag, seal almost all the way, suck the air out w/your mouth while pushing on the bag, then seal completely) and only freeze things you want to cook before eating, because they'll be mushy raw.
We make most of our meals from these staple ingredients:
rice (organic, bulk)
pasta (bought in 5-lb. bag)
frozen broccoli, cauliflower, peas (in winter)
vegs from an organic farm share (in summer)
carrots (always cheap)
cabbage (buy 1 or 2 on sale; slice thin and freeze)
onion (always cheap)
tomato puree (I buy the gigantic can, make spaghetti sauce, and store it in jars in back of fridge until ready to use--lasts about a month, and we eat a lot of spaghetti)
peanuts, cashews, almonds (organic, bulk--good protein if you're not too concerned about fat)
canned kidney, black, green beans
orange juice (from frozen concentrate)
canned corn, pumpkin, apricots, pineapple (in winter)
fresh fruit (whatever's in season and comes from fairly nearby)
cheese (not the healthiest, but good protein in moderation)
eggs (always cheap, esp. the 18-pack)
plain nonfat yogurt
quick-cooking oatmeal (organic, bulk)
raisins (organic, bulk)
powdered instant soymilk (organic, bulk--add to oatmeal, batter for baking, creamy soups, etc., for extra protein)
whole-wheat flour and brown sugar for baking
soy sauce (giant can from Asian store)
plenty of spices (way cheap in bulk--favorites are garlic, ginger, oregano, cinnamon)
Hope that gives you some ideas! Happy eating!