Very new to salt water .... took the advice of local pet store guy and I'm embarrassed to say I filled my tank with conditioned TAP water!!

All I have is water and live sand in my tank. PH, Ammonia, Nitrite all fine for 7 days. Nitrate 10-15! Tested my Tap.....10-15! I was told this water is fine to cycle with and fine for fish only tank. I want inverts. Do I put live rock in with this level and allow to cycle? Or do I make a big water change with distilled water, let cycle, then start adding rock, fish, then inverts, essentially starting over? The guy at the store said algae can fix my nitrate problem, what does he mean? He also said I'd be doing lots of water changes before adding fish?? I'm not thrilled with the idea of carrying 10 gallons of water out of the grocery store. Is my next option to buy a RO system? I saw this one in another posting
Aquarium Water Quality: Pure-Flo II RO Units
Are the RO systems from say home depot the same as ones sold for aquariums? Lots of questions!!! Sorry!

Tank is 29 gallon.