Depending on the space, weather and sunlight you can grow any herb. Most balconies are limited in space and sunlight so not everything will grow. The best herbs to grow on your balcony are basil, chive, dill, fennel, lavender, mint, oregano, parsley, rosemary and sage because they don’t require much space nor direct sunlight. I would recommend to pick a couple of favorites, you can always add more later.
Never buy grocery store herb plants! These often have underdeveloped roots and will die quickly after purchasing them. It’s better to buy your herbs from a garden center because these have healthy roots systems. This has less growing time than seeds. But the best way to grow healthy plants is to grow them from seeds. This takes the longest but to me is also the most satisfying. The first time I tried this i was a bit over enthusiastic and sprinkled seeds everywhere. Now I know better: don’t plant them too close together. This will make them suffocate while competing over the little available soil in your pot.