Many common fish diseases will primarily attack stressed fish, and providing your aquarium inhabitants with a safe and restful environment that is similar to their native home is therefore a very wise decision. There are however many fish species that should not be kept with plants since they will destroy them. There are also many fish species that will feel more at home in an aquarium decorated with rocks and caves, or empty sea shells, than with plants. (You can of course combine live plants, rocks and empty sea shells in the same setup.)
If you are a beginner aquarium keeper, or have not kept live plants before, you should ideally begin with sturdy plant species such as Java Fern or Amazon sword. These plants can adapt to a wide range of different water conditions, which means that you can place them in most aquariums regardless of exact temperature, pH and hardiness. They are also sturdy enough to withstand nibbling fishes, and if a plant becomes uprooted by a digging fish it is usually not a catastrophe for the plant. If your fishes are very fond of digging, you can instead opt for floating plants or plants that can be attached to aquarium decoration instead of being planted in the substrate.
All plants will need light, carbon dioxide and nutrition to survive, but some plants are more demanding than others. The sturdy plant species mentioned above can be kept in an ordinary aquarium with only standard aquarium light, no added carbon dioxide and no fertilization. If you choose plants that are native to clear waters or plants that grow close to the surface in very sunny regions of the world, they can require very powerful lights, such as fluorescent bulbs or metal halide. Between these two extremes you will find the moderately demanding plant species that need roughly twice as much light as the standard light in an aquarium.
A common recommendation for moderately light demanding plant species is 20W for each square foot of tank surface area, or 2W per gallon of water. These recommendations are however quite vague and the only way to find out exactly how much your particular plants need is of course to research each plant species. The necessary amount of light will also be affected by other factors, such as how densely planted your aquarium is and how far down the light has to penetrate.
As mentioned above, all plants need light, carbon dioxide and nutrition to survive and if you adjust one of these three factors you will often need to adjust the other two as well. Never add extra light without first finding out if you need to add more nutrients and/or carbon dioxide to the water as well. Carbon dioxide and nutrients are naturally produced by your fish, but for some plants species this is not enough and they will need additional carbon dioxide and/or fertilizers to be able to fully benefit from the increased light.