Genetically modified (GM): Because most genetically modified crops are grown commercially (corn, cotton, soy, canola, and sugar beets are the primary GM crops on the market now), it's unlikely home gardeners will ever buy them, the two exceptions being summer squash and maybe sweet corn. But it helps to know the difference between hybrid and GM seeds.
Unlike hybrids, which are created when two plants are cross-pollinated to make a third plant, GM varieties are plant varieties that were created by the insertion of genes that may have come from another plant, a bacterium or other microorganism, an animal, or even a lab-created gene. The genes can be inserted by creating a tumor in the original plant or by using a "gene gun" that literally shoots new genes into cells of an existing plant in a petri dish—a process as far from natural as you can possibly imagine.
Though you may never buy a GM plant variety, the chances of getting varieties with GM genes in them by accident, however, can be high, especially for vegetables that are closely related to widely planted GM commodities, such as field corn, soy beans, and beets. Stick with standard or older hybrid varieties of summer squash and corn to avoid getting GM varieties. Unfortunately there isn't much you can do to completely avoid stray GM genes in the other veggies mentioned, especially any type of corn seed (corn pollen can travel for miles on the wind), except not grow them at all—another reason we need to put tighter restrictions on GM crops.
Open-pollinated: These are plants that are created in the most basic form—pollinated by either bees or wind. Unlike hybrids, open-pollinated seeds will reproduce true to type, meaning the offspring will display the same characteristics as the parent plant, and seeds can be saved from season to season. However, if you save seeds from an open-pollinated tomato variety and you live in the northeast, your subsequent tomato offspring might taste very different from the same tomato grown by a gardener living down South. Your variety has adapted from elements in your particular climate and environment, and theirs has, too.
Heirloom: Just exactly how long a standard variety has to have been around to be called an heirloom depends on whom you talk to, but the end of WWII is a generally accepted cutoff point. That marked the advent of chemical-dependent agriculture and the selection of varieties that grew well in those conditions. Heirlooms can be great choices, because they were developed to grow well in organic conditions. They have also pleased generations of small growers and gardeners well enough to have survived, so they are usually easy to grow and tasty. All heirloom varieties are open-pollinated (though not all open-pollinated varieties are heirlooms), and that means you can save seeds from this season's harvest to plant next year.
So which kind of seeds should you buy? Shop organic when you can. Other than that, buy varieties that appeal to you and have characteristics that suit your needs and your growing conditions, whether they are hybrids, standards, or heirlooms. Here are a few places to start looking:
High Mowing Organic Seeds: Heirloom and hybrid seeds, all certified organic
Johnny's Selected Seeds: Heirloom and hybrid seeds, some organic varieties
Seed Savers Exchange: All heirloom seeds
Seeds of Change: Heirloom and hybrid seeds and seedlings, all certified organic