Nitrates & phosphates are removed through water changes and via beneficial algal growth and/or a phosphate reactor; for your purposes, water changes (and maybe a small refugium) should be enough to keep the phosphates down. Keep in mind that phosphates may be present in your tap water, so you'll want to test for them to be sure that your tap water is not at fault rather than something else; this is why it's a good idea to invest in an RO/DI system because it removes the phosphates, nitrates, dissolved solids, etc. from your tap water.
High phosphates and/or nitrates will result in a bloom of ugly nuisance algae Said bloom will lower the levels of phosphates and nitrates, but who really wants to look at the gross green algae when you could have multi-colored beneficial coralline algae growing on your rocks? UV will kill some of the algae, but it most likely will not get it all. The beneficial algae that you want is called coralline algae and is usually purple/pink/lime green/white in color and encrusts on the rocks and other surfaces; all other forms of algae should be avoided in the main aquarium (macro algae can be kept in the refugium).
You'll get to see a few of the different types of nuisance algae & diatoms as the aquarium cycles; they'll clear up as the cycle progresses, and the system becomes properly balanced.
