A note about plants: It's pretty hard to calculate exactly how many plants you need to use up your nitrates, but A good way to sort of figure out an an an optimum fish/plant ratio that I have used is this:
In a cycled (or very small and therefore nearly uncyclable tank)
Buy some easy, fast growing plants. Anacharis (also called Elodea) is very cheap, super hardy, and just the right kind of plant. Buy one "bunch" of plants per inch of fish in your tank, slightly less if you have a well-stocked tank. Rinse the plants well with some tap water a few times, and then rinse with some treated water or old tank water. Plant the plants in your tank substrate, and do your normal routine. For the next few weeks, watch the plants closely, and do NOT use fertilizer of any kind. Test your water and compare your results to your normal schedule.
If your plants explode with growth and look fabulous for a bit, and then kinda level out, you should try adding one or two more plants. Do the same if you notice that in your tests, your nitrates are not lower than usual, or lower than usual but not by very much, and you feel the plants haven't helped much.
If your nitrates have dropped nicely ( they probably will never end up being zero however, except right after a water change) , congrats, you've gotten it close to right! You can add more plants or plants of other varieties if you like, but if you put too many plants in your tank, you'll have to add a little fertilizer of some kind to feed them, since the fish and bacteria won't produce enough nitrate/other things they need to grow.
If your plants go totally insane and do not stop, either buy more plants or take some little cuttings from your little Elodeas and plant them.
If your plants die, or get sickly/yellow/pale, they are not receiving something they need. Perhaps the water is too salty, snails are chowing on them, or they aren't getting enough light. Give your little planties 12 hrs ish of light a day, and 12 hours dark-- they need the dark time, too. Plants use photosynthesis to generate energy during the day, but also burn this energy (Read: grow and make leaves, etc) during the night... so don't give them only dark or only light. Aquarium plants benefit from a grow light or plant light... but they might also be fine with ambient light, or a little sunlight (not direct sun, which can overheat your tank, but sun that comes through the window and still manages to light the tank a bit)
I suggest using Elodea for this only because it is so cheap and hardy, and will grow from cuttings easily. You could also use other plants that are hardy and grow fast. Look up "plant cycling" or "Silent cycling" and use plants that they recommend for that, if you like, because plant-cycling plants all grow fast and in accordance with water parameters.