I started gardening three summers ago completely by chance. I came home from work, and my father-in-law had placed several little plants around my backyard, including tomatoes, cucumbers, and peppers. Little did I know that I would get completely hooked on growing my own food.
If you're going to start a garden, I have a few suggestions:
1. Start with food you like.
2. Start with plants that are easy to grow.
3. Start small, and build on your success.
Start with food you like
You won't be interested in spending time watering, fertilizing, and observing the growth of your plants if you aren't excited about eating the results. If you don't like vegetables or fruits at all, maybe try an herb garden. Herbs are awesome for adding fresh flavors to soups, meats, and casseroles. Personally, I like rosemary, parsley, and basil the best. A little bit of these herbs goes a long way, and most herbs are beneficial for digestion and can help soothe an upset stomach.
Start with plants that are easy to grow
I still haven't successfully grown cilantro, and my dill always dies before I can use it. I love growing
radishes, peas, and tomatoes, though.
Radishes grow quickly, so you can celebrate a quick success while you wait for other plants to catch up. If you have kids, radishes are a great way to introduce them to gardening because they grow quickly and can be harvested easily by your youngsters. The leaves are also edible
To grow peas, you'll need some tall thin stakes or a trellice for the vines to climb, but it's worth this small additional purchase. Peas help the soil by taking nitrogen in the air and fixing it in the ground. This is useful if you grow tomatoes or corn in the same area, because these will take all the nutrients they can out of the soil. Peas grow relatively quickly when it's warm enough, and you can get a real robust crop if you plant new peas every couple of weeks. If you have kids, they'll love pulling the pea pods off of the vine, and you can have a sweet high fiber, high protein addition to your meal within minutes.
Tomatoes are my favorite to grow. You get a lot of bang for your buck with these plants, and cherry tomatoes are particularly gratifying because you get a lot of little fruits growing in clusters of usually 6-8. They'll start of white, then turn green, and are ready to harvest when they're red. My daughter loves to harvest them by just pulling them off the plant. Then we wash and eat them right there within seconds. I recommend harvesting these in the morning so they're still cool and more pleasant to snack on.
Start small
I started with 4-5 plants, and this is probably a good number to max out with at first. To achieve faster success, buy young plants from your local nursery or Home Depot. If you want, save the seeds from some of these fruits and replant them next season. Once you've had success, expand your garden to include a wider variety of plants. In my second year of gardening, I really got into herbs, so I grew about the same number of veggie and fruit plants, but expanded by growing a variety of herbs.
Other tips and considerations
If you don't have a spot that gets a lot of sun in your yard, then buy some pots that can be moved in to sunny areas. Vegetable, fruit, and herb plants all need 6-8 hours of full sun to grow successfully. If you're lucky, you'll have a south-facing wall in your back yard that gets a lot of sun year round. If not, then buy some pots.
If you're planting in the ground, buy some garden soil to mix in and add nutrients. If you're planing in pots, use potting soil. Potting soil holds on to the moisture longer, and soil in pots will dry out faster than soil in the ground. For garden soil, I use Kellogg garden soil. For potting soil, I'm using Miracle-Gro Moisture Control soil. I get them from Home Depot, but you could compare costs with a local nursery to find the best value.
I hope you enjoy growing your garden. Don't overthink it. Just get started and learn as you go.
Cheers!
First up are my chives. I planted these last September, and they are hitting their stride now. I got worried for a couple of months in winter, and I thought they were going to just die, but I kept watering them as needed, and now they are thriving. I love chopping them up and adding them to my salads, soups, and mashed potatoes. 
Here is one of my several mint patches. I started this patch by transplanting some mint that I thought would die when we added several feet of soil to level our backyard. Now this transplanted patch AND the original are growing nice and tall, with leaves as long as my fingers. I'm eating some leaves chopped up in my ramen noodles as I write. 
Next is my oregano. This guy is a fighter. He got too hot and all but died at the end of last summer. Here he is now, bouncing back nicely. I picked off a couple of leaves so Heather and I could sample the powerful flavor of the fresh leaves. I don't recommend this. It burns and numbs the tongue and lips a little. Oregano is great in sauces, and also has antifungal and antimicrobial effects. 
