A greenhouse can support a family of any size, as long as the greenhouse is big enough and the space is used efficiently. It's reccomended that each member of your family is allocated between 15-20 plants each year. If you're only looking to add some sides, rather than completely satisfy hungry mouths, between 5 and 10 should work. Greenhouses can range from small cold frames, all the way to giant, sprawling conservatories. Almost any budget can afford a greenhouse, as they are incredibly easy to DIY, and so flexible in their sizing.
Greenhouse can also be used to turn a profit in order to financially support a family. Excess produce can be sold directly at farmer's markets, roadside stands, or to farm-to-table restaraunts. Secondary products can also be made, like jams, jellies, baked goods, ciders, etc. Even a small profit can mean a greenhouse is able to pay for itself, making an impact on your family's overall income and ability to spend.