If you ever grow vegetables the normal way, and once you have mastered how to deal with mildew and other diseases, as well as insects and other fauna, you will easily see that a plot 20′ by 20′ gives you enough veggies to feed your family twice over. In your home, it is likely that you have a room which is 15′ by 15′ or bigger. If, in that room, you go up walls and poles with little holes in them and grow both vine plants and non-vines in small containers, you will have a crop that is 15′ by 15′ and 15′ by 15′ and 15′ by 15′, as many levels as will fit. You will have the same number of plants as on the floor again and again on the different levels. If you have a skylight, there is no problem for the light to reach down. If you don’t, you can bring in gigantic amounts of light with large clusters of fiber optic cables; it has been done again and again in underground houses from Tokyo to Mexico City. It has also been done with mirrors, but the fiber optic system is easier.
The problem you will have is the same as with a greenhouse: your plants will normally be more protected than outdoors but, if a virus or whatever does get in, the whole crop will be wiped out quickly. If it happens, just start over with a different crop. You will normally be successful.
The same as, for several years, there has been a rage for square foot gardening, there is now one starting for vertical gardening. Check out their websites, and you will have their math coming out of your ears. But the best is simply to do the gardening. It’s easy and it works.
You can also check out lasagna gardening, with no soil, just layers of paper. And you can combine methods.
Then enjoy the fresh food.