You definitely need live rock. Live rock will serve as your #1 source of filtration. If you wanted to save cash, skipping the live rock was not a good choice. You should get 1 to 2 lbs of live rock per gallon -- so 30 to 60 lbs. To save money, get a few lbs of live rock, and buy the rest dry. Once you add it to the tank, the live rock will colonize the dry rock, and the dry rock is much cheaper than buying it live.
Power filters are not meant for saltwater and tend to cause water quality problems. A better choice would be to get rid of the power filter and fake coral and buy rock instead. The rock will give your fish all the hiding places they need.
The fake coral will provide nothing for filtration, so it can't take the place of live rock.
It usually takes a tank at least 3 weeks to cycle. Every tank is different, so you'll need to buy some test kits to keep track. The basic tests you'll need are ammonia, nitrite, nitrate, pH and alkalinity. Once ammonia and nitrite are at zero, then your cycle is over. Only add another fish once the cycle is finished.
Good luck and keep us posted!
