Grow for flavour instead of cost.
You won't ever beat the taste of tomatoes that actually ripened in the garden, or real new potatoes that you can rub the jackets off with your fingers, sweet tender baby carrots from thinning your carrot patch...
I suggest Nantes carrots, Bib lettuce, Bonny Best or Best Boy tomatoes, Lincoln green peas and "Peaches and Cream" sweet corn.
Young beets the size of golf balls or a bit larger cooked with their tops are a treat. (Detroit red or cylindrical beets)
Swiss chard, spinach, mustard and all those other greens.
Yukon gold are good potatoes and so are any of the Pontiac type red potatoes.
For squash I really like the Hubbard and the acorn squash. Don't grow more than 2 plants of black zucchini unless you have recipes for zucchini relish, zucchini cake, zucchini muffins... because zucchini is hard to keep up to.
Hubbards take up a lot of area but they can crawl where they like over a lawn or other wasted space
Don't forget your herbs and spices, fresh basil is a much different thing than the dried stuff.
If you grow chili peppers they make lovely garlands. Sew a strong thread through them and hang them up to dry in the kitchen. Then you just break off what you need when cooking.
Garlic is easy to grow and you store it by braiding the tops into a rope with the bulbs sticking out and hang it up too.
I like berry canes,(rasberry, himalaya blackberry, etc) and strawberry plants. Currant bushes are fast producers too.
Even though they take a few years to produce small fruit trees like Weeping Mulberry, dwarf apple, dwarf cherry are good things if you have the space.
Crops like Rhubarb and Asparagus are easy to keep once they are established, but they should be let grow for two years before you start harvesting them heavily.
Flowers are nice to grow.
Not only will they look nice but some like Nasturtium, Violets, Day lilies and Roses are nice in salads too. (Pluck the white part off the rose petals to avoid bitterness, Nasturtium is the same as Watercress)
Don't forget that squash blossoms can be eaten.
Don't try planting seed from store bought vegetables because most of it is hybrid or carries plant diseases.
Buy Natural or Heirloom seeds and you can save seeds from your own garden to plant the next year.
About weeds. One of the first things up in the spring is Lambs Quarters (Chenopodium alba) and it is a better spinach than spinach is.
I also suggest you look at hazel bushes. They make fairly good hedges and produce hazel nuts.
Maybe I should point you at an edible landscaping site or two.
http://www.ediblelandscapes.ca/http://ediblelandscaping.ca/Here is Burpee seeds. They are a noteworthy seed catalog that will give you lots of ideas
http://www.burpee.com/I am sure your search-fu is good enough to find more.
The problem isn't with suggesting what to grow, it is with suggesting what not to grow.
I would say not to bother with pineapple and coconuts in New York state.
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One last thing is that some plants are for arts and crafts. Things like hardshell gourds, ornamental corn, garlic braids and so on can be quite profitable hobbies.