You don't need a lot of room to grow a lot of food. Do you want to provide all the food short of say staples you have to buy for 2 people? I'd say a garden that is 4000 sq ft will easily do it. Do you want to supply a large percentage of your food? 2000 sq ft would be enough.
I provide most of my food all summer thru fall (june thru october) for 1 person on 1200 sq ft and a reasonable amount for the remaining months of the year and I don't can anything and freeze a minor amount. I think it depends upon what you grow too.
For example if you can or freeze pole beans or tomatoes it doesn't take much space to grow literally tons of them. Cabbage also can provide tremendous amounts of food in a small area but you'd have to make sauerkraut to keep it more than 3 months as they start to go off in a fridge. Rutabagas keep for several months in a fridge. Onions and garlic, carrots and beets as well can provide all you can eat for a year in a small space just pick varieties that have long storage ability. Winter squashes also provide a lot of food that stores from 3-7 months depending upon varieties tho they take a bit more room but you can crowd them and they seem to do ok as far as yields. Lettuces, swiss chard, most greens can produce all winter if you have a greenhouse tho at a slower rate. Broccoli can produce all season into freezing temps and it freezes well. Yellow squash and zucchini will produce by the ton and can be frozen. Cukes are hugely productive but you'd need to can them, even fridge pickles last only about 120 days.
Avoid things like melons, brussels sprouts, cauliflower, anything that produces 1 crop but takes all season as these are space wasters. Potatoes are iffy, they require a lot of space for the meager yields (1-4 pounds per plant) so I stopped growing them. Guess why they grow them in northern Maine - lots of empty space and poor soils. Corn takes a lot of space and attracts a lot of trouble (deer and coons).
This is a lot of work, don't fool yourself that this just happens. Weeding is time consuming and many crops I mentioned do not compete well with weeds, this is where raised beds that never are tilled are a blessing. Watering can take a lot of time, no water, poor yields except for garlic which does not need much water and neither do tomatoes. Want to go on vacation for a week? Maybe but 2 or 3 forget it. But you can save a ton of money and growing organically is not difficult and you can be assured your food is free from toxins that are on and in store bought food.
Garlic and winter squash are stored at room temp. Onions can also be stored at room temp for months tho after 3 months I move them to a fridge. Carrots, beets, cabbage, rutabagas, potatoes all require a root cellar or fridge, an extra in the basement helps me. I store garlic and onions there as it is cooler and winter squash until the temperature drops to 57 then I move them to a cooler place in the house where it is 60-65 all winter.
Seeds are cheap and last for years tho onions seed is good for 2 years at the most and I buy it fresh each year. I use maybe a gallon of Neptune's Harvest Fish and Seaweed emulsion for 2 years. Promix for starting seeds is expensive tho and you need shop lights and a cheap grow light stand to grow plants. I made one from pvc pipe, I have directions if you want them. Window sills are useless to grow plants and if you buy plants you'll spend a lot of money. Once you buy the tools they last - shovel, bow rake, stirrup and regular hoe for weeding, a sprayer for fertilizing, a rototiller is expensive but allows you to do it when it needs to be done and a wheel barrow are the basics. I have a chipper shredder too and use it in the fall, they cost and are not really needed but are nice to have especially for making shredded leaves to mulch.
It ain't fer everybody but the results are satisfying when fall comes and you have a lot of food plus you ate all summer for free.