The benefits of vegetables are largely in the antioxidants. The way that they react with human cells is only beginning to be understood, but it is thought that they absorb the free radical particles that destroy cells. Science makes new discoveries all the time about the details of the process.
One very simple rule is that bright colors are healthy. Orange is beta carotene. Blue/purple is anthocyanin. Red tomatoes contain lycopene. Cruciferous vegetables like Broccoli, Cauliflower, Cabbage, and Kohlrabi also contain healthy antioxidants and phytochemicals. Green tea deserves a mention, and many mushrooms as well.
The "organic" label is meaningless now that the government took it over. Under NAFTA, the US is not allowed to question the authenticity of any labeling of imported produce. Mexican growers can coat their product with pesticides that are illegal to buy in the US. If it is labeled as organic, they make twice the profit, and there's no risk of getting caught. But small farmers in the US get inspected so rigorously that it's often not worth it to obtain the necessary government approval for the "organic" label.
What you really want is fresh food, and the closer you are to the production of it, the healthier it is. Your local farmer's market will have the freshest food.