I would say tomatoes, for two reasons:

1.) They are pretty easy, and
2.) The payoff is so high—the difference in taste between a storebought tomato (which often resembles red styrofoam) and a fresh tomato out of your garden is so great that it will convert the most lukewarm gardener into a passionate horticulturist for life.

It depends on your specific conditions.

For example, how much sunlight, are you growing in the ground or in containers, how much effort do you want to put into them?

Of course grow something you like, though not necessarily something you “already like” because some commercial vegetables taste like crap, while fresh don’t. Tomatoes are the best example of that.

Triv is correct about tomatoes being good if you want a big payoff. Just a few plants will produce so many tomatoes that you need to give them away to your friends, thus allowing you to brag (involuntarily, since you don’t want to waste them) about what a great gardener you are.

Peas and beans are good for infertile soil, or where it doesn’t get very warm, or if you’re growing in the spring or fall. Broccoli and cabbage are great if it’s really cool, or you want to grow them over the winter. Carrots and parsley are good for that, too.

My favorite is the growing of Basil. There is a bunch of different kinds, each obviously special. You could have an herb garden solely of different kinds of basil and it’d still seem amazing. For example, lemon basil really smells strongly like lemon peel (it has the actual same chemical in it as the real thing), cinnamon basil smells like cinnamon, licorice basil smells like anise (again, the actual same chemical), lettuce leaf basil has huge, milder-tasting leaves you can put directly in salad. There is purple basil, blue basil, there are kinds which smell like cloves, and others which are very much like camphor. And they all grow very easily.

Herbs are, quite literally, weeds. You can even grow them in between other plants, and they’ll do a lot of the work for you, keeping the ground moist (by providing cover), preventing bad weeds, keeping away insects (many are repelled by their scent), attracting anti-pest predators (who associate the strong smell places pray might, ironically, go), et cetera.

I started out growing sugar snap peas in containers on my apt. patio, very easy and since they are expensive a good investment. Need support, though. Chives are also easy, I started some seeds 5 years ago and they are still growing in the same container, same soil and no fertilizer. Tomatoes also do well in containers. Red and green peppers are also easy to grow, just remember to water.

potaotes are really good to break up the soil, and onions are realy easy to grow from sets. rocket also grows really quickly, and is great in salads or on pizza.

cherry tomatoes practically grow themselves.

and rocket (i think it’s called rugola elsewhere?) is called that cause it grows like a rocket!

Always grow what you plan to eat. Tomatoes are very persnickety depending on where you live. Because of the weird weather, my tomatoes have had limited output. All the rain about killed them. I have two varieties of tomato growing in the same ten-inch pot: cherry and patio. Surprisingly, my bell pepper was doing well, that is, until the rain! So I would start with tomato and bell pepper, because almost everybody likes bell pepper, but I wouldn’t start NOW, because it’s a little late for the season!

I’d forget root vegetables unless you’ve got space for them. And take into account your climate, too. I’d dearly love to grow my own leeks, because I love them, but it gets far too hot in Oklahoma for them to survive.