The ingredients you use to make your food are the most important thing. This is true both at home and at a restaurant. You can have the best chefs working for you, but if your ingredients are sub-par, it's just not going to be as good. It's kind of like starting with a sound foundation when building a house. This is not to say that your dish will turn out perfect if you use good ingredients: you can still screw up the recipe, burn it, or plate it in one big soggy mess.
When buying produce, my big two watch words are organic and local. Organic products are USDA certified and should have a little label on the packaging somewhere. They are produced using methods that do not involve modern synthetic inputs such as synthetic pesticides and chemical fertilizers. Organic foods are not processed using irradiation, industrial solvents, or chemical food additives. However, in the United States, these may include genetically modified organisms (GMO's).
The term "local" used in conjuction with food is not regulated like the term "organic." However, it generally refers to food that has been grown in a radius of about 100 miles. The best source for local produce is a farmer's market. The benefits of locally grown foods are legion. However, to me the most important reasons are taste (they haven't been artifically ripened and were usually picked within the last 24 hours), less fossil fuels burned to ship them to my table, and the money I spend stays in the local economy.
Usually you will have to settle for one or the other, since not all organic produce is local and not all local produce is organic. In some cases the farmers at your farmer's market may actually grow their produce in line with organic practices, but just don't have the money to pay for the USDA certification. It always helps to talk to the guys and gals manning the booths and maybe even take a trip out to a farm.
Another source for local foods is a CSA (community-supported agriculture) subscription with a local farm. You can find these by going online and searching for CSA memberships in your vicinity. CSA members or subscribers pay at the onset of the growing season for a share of the anticipated harvest; once harvesting begins, they receive weekly shares of vegetables and fruit, in a vegetable box scheme, and also sometimes herbs, cut flowers, honey, eggs, dairy products and meat. Some CSA's deliver straight to your door step, others deliver to a set spot in your city, others require that you come pick up your share at the farm. Some farms will also allow you to go and pick your own produce, especially at the end of the season when they are trying to clear their fields.
And of course, what better way to get fruits and veggies than by growing your own. Not only do you have control over the kind of soil you purchase, but you also know exactly what kinds of pesticides and what kinds of fertilizer you use. The best fertilizer is compost (either from your own compost heap/barrel or bought in bags) and instead of using pesticides use some diatamous earth around the outside of your beds to stop grounded pests as well as a combination of crop rotation, close monitoring to spot issues immediately, and companion planting (i.e. planting marigolds near tomatoes to keep aphids away). There are many websites and books on the subject of growing safe veggies, herbs, and fruits in your own backyard.
The amount of labor involved depends on the types of produce you decide to plant given the amount of time you think you will be able to put into maintaining the garden. You also don't need a huge backyard, many people make do with planters on windowsills and balconies. Climbing plants like squashes and cucumbers can also be grown in pots and then trained up a wall. Things like mint, should be grown in pots, if you don't want it to take over your whole yard. The time and effort will be well worth it when you are serving cucumber salad or mashed potatoes made from produce picked in your own garden.