10 Gallon Nano reef (new to saltwater)

Hello everyone. I am new to saltwater and need a few things cleared up for me. I have done about two months of research trying to figure out if I can create this tank due to the amount of care it needs and amount of money it will cost. I am a biology major in college so im on a budget. I am looking to start with a 10 gallon tank with a 10 lbs of LR and LS, a 75 watt heater, and a 245 koralia pump. I want to eventually turn it into a reef tank. Live stock would be flame goby, lawnmower blenny, maybe a small clown, and then pack it with shrimp crabs, and snails. I am looking at a quad t5 fixture for the tank as well. My question is whether or not I actually need an external filter for the tank or if that will cause nitrate build ups. Also I was looking to save money by buying 5 lbs live rock and 5lbs dry rock, how long would it take for the dry rock to build up the bacteria. Thank you for your help :D