It is first important to note that plants use photosynthesis for growth. In doing this, they have light requirements. Amount of light and Watts per gallon are useful measurements, however, the most important light requirements are color and PAR value. For standard T-5 or T-8 type lights, you'll want temperature color 6700K. This is light that is similar to noon with no clouds. 5500K is daylight and 10,000K is full spectrum (blue). For LED lighting, you want to pay attentin to wave-length. You'll want to get as close as you can do Red 640-670nm and Blue 430-460nm. You'll want more blue than red, anywhere from 60%-40% to 75%-25%.
Plants eat up plenty of nutrients to grow. In doing so, they reduce the bio-load needed to be handled by filters. Ultimately, you'll want to follow the standard filtration requirements of your stocking. However, what you'll want to pay attention to with which plants you get is how much water flow will be occurring where they live. Rooted plants can handle a lot of water flow (similar to a sword plant with a powerhead near it). However, stem plants without roots will be knocked over by high water flow. If they are short you can angle your filter output away from them, however if they are tall you'll need to find a way to secure them or deflect water flow.
You'll want substrate that the plants can attach to and anchor themselves, or you'll want to anchor them with "lead" or other plant weights. You can also anchor certain plants (anubias or microsorum) by attaching them to driftwood or rock via cyanoacrylate gel (super glue gel) via the rhizome. These plants will then attach themselves via their roots and the cyanoacrylate will eventually dissolve (fish safe).
With plants, you can usually create a great environment for most fish. Mid- to top-tank dwellers will enjoy tall plants (echinodorus or ludwigia) whereas bottown dwellers will enjoy shorts or bushier plants (cryptocoryne or hygrophila in addition to what's been mentioned). It is important to note that if you pick fish that sift substrate or get large (pleco, clown loach), they will dig up plants or knock them over, so pick strong rooted plants with these fish. There are also fish that eat plants (gold fish, some plecos, etc) so you'll want to check on that to see what they prefer in case you need to avoid plants or pick tougher ones.
Depending on the above factors, you'll want to pick your plants. There are a lot of "low light plants" that work well without high light. These plants are usually green plants (vs red or purple). These are also usually the same types as the "beginner plants". These go by the Anubias name or "crypts", "java fern" and "hygro". Taller, strong rooted plants are normally called "swords" and do well for beginners and some even in low light. It's difficult to cover all the possibilities, but what I recommend is looking through plants, picking the ones you like and then researching them before buying. Make sure you can keep them alive in your conditions.
Ultimately, there are so many factors in planting your aquarium that there are literally books about it. Be sure to research your fish and plants and then set up your aquarium based on their requirements. I recommend a low light or beginner plant stocking at first. You'll find these easier to keep alive and easier to enjoy. Once you learn what you like, you can expand your equipment or plants to suit your needs. You can work with fertilizers or high light, maybe injected CO2. These advanced topics are a lot of fun if you enjoy them, but don't let them intimidate you at first! I run low-light sword tanks (among others) and they look just fine -
Just remember to have fun with it!