I have several interconnected suggestions for you -- and thus a rather long post. I also want to salute your willingness to take this on and try to cook at home more often. Saving money is most definitely possible, but you’re right: it’s trickier than it looks by a fair margin. You can do it, but a lot of it comes down to knowhow.
I’ll start with a recipe for you. You’ll love this — everyone does. You know how you end up with little bits of cheese that eventually start to grow fur? Okay, so cut off any fur, wax, nasty dried-up bits, and so on. Cut everything else into medium-small chunks — or you can put them all into the shredding blade of your food processor if you like. Dump the pieces into the processor, armed with the regular metal blade. Add about 1/4 cup of white wine to start with. Pulse the mix until it’s starting to come together, then run it full-blast until it’s smooth. Pack this into a crock, cover tightly with plastic wrap pressed right against the surface, and refrigerate. To use, spread it on crackers. If there’s still a certain amount of it when you next have some cheese chunks, just re-process the whole mix. If it doesn’t want to come together, add a dab more white wine. If it’s too liquid, add more cheese. If it seems dry, add a little butter. You can keep this stuff going for a good long time. In winter, you can also cook a batch with a little bit of garlic over very low heat and you’ll have some darn good cheese fondue.
A small tip on vegetables. You DO NOT save any money by buying bulk potatoes, onions, shallots, or other root vegetables, unless you use them constantly in large quantities. These vegetables respond to light by sprouting, which makes them of not much culinary value. But your supermarket stores these things in light. So when you buy 10 pounds of potatoes, and store them in a dark place, they are likely to start sprouting within a week. Don’t do that: buy these things when you need them. Another vegetable tip: fresh tomatoes in the supermarket usually cost a mint and taste horrible. If you’re going to cook the things, buy good-quality canned — and Hunt’s is quite good quality, as well as cheap.
On to freezing. With some exceptions, the higher the fat content, the better it will freeze in a home freezer. Meats and such should be wrapped in butcher paper to help prevent freezer burn, but on the whole they’ll do very well. Vegetables do not freeze well, as a rule: to make them freeze well, you really need special equipment. If you just bung a head of broccoli in a bag and freeze it, it’s going to come out like your worst memory of why you didn’t like to eat broccoli when you were 5. Seafood is quite tricky to freeze; I would avoid it until you are feeling a lot more confident and are faced with an excess of something.
What usually goes wrong with freezing meats (including poultry), assuming you’re being reasonably assiduous about wrapping and such, is that the texture gets dubious, and sometimes the appearance isn’t ideal — freezer-burning gives you the worst of both worlds. Meat like this will be fine as soup stock, however. One reason this happens is that quite often you’re freezing meat that has already been defrosted once, by the supermarket. That’s not doing anything good for the texture or appearance. But again, it’s fine in soup stock.
Which brings us to my next point: soup stock.
When you cut carrots onions, celery, tomatoes, and so on, you will end up with scrap ends. Keep a medium-sized tupperware beside your board as you cut, and throw all these ends into it. In between cutting sessions, store the tupperware in the freezer. When it is completely full, it’s time to make soup. You can put pretty much anything in, but avoid greens (spinach, lettuce, collards, etc.), head vegetables (broccoli, cauliflower, etc.), and any kind of peppers (hot or sweet, any color). If you forget and leave half an onion in the veg drawer a little longer than you should — not so it’s moldy but so it’s kind of soft and not what you’re looking for in a dish — bung it in the tupperware. This trick will save you money, to be sure, but it will also give you the pleasure of watching yourself save money.
Another trick that is a benefit of cooking for two: save your bones. When you serve T-bone steak for two, put the bone in a freezer bag when you do the dishes. Same with pork, chicken, and so on. Not fish — it doesn’t work well — but if you splurge on lobsters (actually quite a good buy these days) DO save the shells (not in the same bag with those bones, though – ick). Whenever you have trim of any kind, ask yourself whether it has good flavor in it, and if so, save it for soup stock. (The trick with lobster shells, incidentally, is to make an intense lobster stock out of them ASAP — they don’t freeze very long — and then make lobster risotto with it. Two lobster dinners for the price of one!)
The next part of the whole soup-saver trick is learning to cut your own poultry. You don’t save much by cutting your own meat or fish — in fact, you can actually lose money by cutting red meat, because the bones and fat are such a big percentage. With fish, it depends on the market: a good market often cuts more or less to order, and they weigh before cutting, so you pay the same whether you cut it yourself or not. A place like this will give you the bones if you want them, usually, so it doesn’t gain you much to do it yourself, unless you enjoy it or catch your own fish. But you can save a huge amount by cutting your own chicken. What’s more, the quality will be a lot higher, because uncut things pretty much always last better than cut ones, and you will also cut properly instead of throwing a mostly-frozen bird onto a band saw. Any fool can learn to cut up a chicken perfectly respectably, and after you’ve done it a couple of times it’s quick and easy. I strongly recommend learning to do it by watching and/or reading Jacques Pépin on the subject; lots of the instructional videos you’ll find online do it very badly indeed — it’s disgraceful. Cutting a chicken will yield a carcass and usually wingtips, as well as giblets, that go into a big freezer bag for soup-making. Everything else you can cook tonight.
So, finally, make friends with chicken. As a cook for two, the chicken is your ally. A cut-up chicken can be prepared a vast number of ways, and a “broiler/fryer” (about 4.5 pounds uncut, these days) should serve two adults with not too much leftover unless you serve a really heavy sauce or something. You could also serve the dark meat one night, fricasseed or fried or broiled, and then the next night cut and pound the breasts to make chicken piccatta or roulades.
If you really want to feel economical, and you’re not especially squeamish or something, I have two great chicken things to recommend. When you look around the sides of the big opening on a chicken, you’ll see two biggish thick fat pads, which you normally trim and chuck. They should weigh about the same as the liver, which too many people chuck, and which you should NOT put into your soup. Mince the fat pretty fine, throw it in a small heavy pan with salt and pepper, and cook it medium-slow until it’s mostly rendered (a puddle of fat with some lumps and not a lot of sizzling water). Put in the liver, cut into lobes, and cook it in the fat, turning occasionally, until it’s just barely done — it’ll still be pink in the middle. If you have a little minced shallot, scallion, or onion at hand, you can cook this at the same time, but it’s not necessary. Add a small splash of white wine or cognac if you like, and cook off most of the liquid. Now scrape all of this into the food processor and wait a few minutes for it to cool of a bit. Process, scraping it down a few times, until it’s quite smooth. Taste: it should be over-salted somewhat — this is necessary. Put into a wire strainer and work it through with a rubber spatula, then pack the strained stuff into a ramekin or other small bowl, cover tightly with plastic pressed right on the surface, and chill in the fridge. Spread on crusty bread and revel in the fact that you were probably going to throw this stuff away; if you used a teeny bit of cut onion end and a small splash of last night’s white wine, or skipped either or both of these things, this dish is basically free. Nice, huh?
The other great chicken thing is a little more of a project (the mousse you can make in just a few minutes, and the processor and fridge do 90% of the work), but it’s just time, not work. When you’re trimming your chickens, you will get a certain amount of excess skin and fat. It’s not absolutely necessary, but it is best to remove this before freezing the bones for stock: you don’t want more fat in your stock than you can avoid. So what do you do with it? Cut it up medium-coarse and freeze it. It’ll last a good couple of months. Now when you have a whole bunch, thaw it in the fridge overnight, then dump it in a large, very heavy skillet (cast iron is perfect) or pot, together with about 1/4 cup of water. Put it over medium-low heat, and wait, stirring occasionally, until you can see that a fair bit of the fat is melting and the water is gently simmering. Put the pan or pot into a 250F oven. In 15 to 30 minutes, check on it: the water should still be simmering, not boiling fast. Adjust the temperature as needed. Now wait an hour and stir. Probably it’ll need another hour or more. What you’re waiting for is you want it to stop simmering or sizzling (meaning the water has fully boiled off), and you want the fat chunks to be a beautiful deep golden color throughout. When this has happened, remove the pot from the oven and wait about 15 minutes for it to cool a bit, then strain the mixture through a wire strainer into a heatproof glass bowl or measuring cup. Let it cool on the counter until it’s lukewarm, then pour it into a tupperware, cover it, and put in the fridge overnight. Tomorrow you’ll find it’s frozen into an ivory-white block. Freeze. You now have lovely cooking fat, which you can use instead of oil in all kinds of savory cooking as well as in savory pie crusts and the like. It’s supposed to be healthier than butter, and certainly than shortening; it takes heat quite well; it tastes fabulous; and best of all it’s essentially free. Oh, and if you want, you can take the golden-brown cooked fat remnants, spread them as thin as you can on a cookie sheet, and bake them at about 300F for another 10 minutes or so to get them really crispy — then toss them with a little salt and let drain spread out on paper towels. These chicken cracklings, crumbled up a bit, are terrific in salads, infinitely superior to those disgusting premade bacon bits, and again, they’re almost completely free.
If you do all of what I just described — the mousse, the fat, the crackling bits — with a duck, you will have created two culinary gems (the mousse and cracklings) and some true culinary gold (the fat). Goose is even better if you can get a good one, but that’s not so easy.
Once you get into this sort of thing, there are lots more ways to be economical. But to my mind, your best thing is to change your habits a little bit. In the process, you’ll learn some excellent technique, making all of cooking a lot more fun. Besides, there is something remarkably enjoyable, in my experience, about serving an elegant meal to your parents or in-laws, and knowing that actually the entirety of the meal cost less than the bottle of wine they brought — and also knowing that they absolutely do not realize this. I still remember the time I served my parents chicken liver mousse with homemade bread (boy is homemade bread cheap!), a salad dressed with a partly-chicken-fat vinaigrette and sprinkled with chicken cracklings, and a whole chicken en saucisse stuffed with essentially the leftovers of last night’s salad, served with a beautiful brown pan sauce from the stock. Cost of dinner to me? $4.75 — I couldn’t resist calculating it. I LOVE that.