To pick corals for your aquarium, there's a ton of corals to choose from. If you're a beginner, I would go with soft corals, namely zooanthids and leather corals and mushrooms, things that are soft, that don't have a calcium structure like a hard coral does. When these corals die, they don't leave behind a structure, a skeleton, like the hard corals do: that's so you can identify the easier-to-keep corals from the more challenging. If you are an advanced hobbyist and you know what you're doing, you monitor your calcium and your alkalinity, and you have the confidence that is required, and the budget to keep some of these more sensitive corals, then you can go with most of the corals that you see at a regular aquarium shop or an online store.
That being said, some corals get really large, and most corals have a defense mechanism where they will sting another coral if they come in contact to it. You want to make sure that the corals you pick are all safe if they do touch each other. A lot of soft corals can grow together and they don't hurt each other, but certain corals will harm each other, so you want to make sure that the corals are compatible that you are going with. But the biggest thing is the needs of the corals. Some corals are not photosynthetic and will rely on heavy feedings on plankton and fish eggs and lots of coral foods. Those are the little more challenging, and you should pick the brains of the people you are buying the fish and coral from. Most corals that you'll encounter at a store are photosynthetic, so if you have good lighting in your tank, those corals should do fairly well in your aquarium. Again, just maintain good water chemistry; that's the key to keeping these corals happy.