First, buy QT'd fish and don't panic, it doesn't have to be scary. Setting up a reef tank can be rather simple and/or complicated, but if you're just starting out, it's better to go slow. If you're starting out with dry rock, it's going to take time, but if you're starting out with established rock or cured live rock, then the biological filter is ready from day one. I would not start broadcast feeding coral food, that's an algae outbreak waiting to happen, but do monitor your corals for signs of stress. Pale colors, healthy looking flesh, not deflated (for some corals), etc...observation is key here, not numbers. People who give you hard numbers are probably the people I would shy away from, because they lack the experience to know otherwise. It's better to stick to ranges and keep them stable (some parameters require tighter ranges). Testing zero NO3 doesn't mean you're actually at zero, if you were at actual zero, things would start to die and fade quickly. Other organisms utilize nitrates more efficiently than corals do, especially algae, so testing zero can mean a lot of different things. Remember, when testing nutrients, you're testing residuals, not actual. Hobby grade test kits are not that accurate, so it's a range, not precise numbers here.
It's a new tank, so there are a lot of biological processes going on that uptake nutrients, alk, etc....it takes time for this to balance out. So don't start dumping food in hoping to raise nutrients, just safely add another fish or two and feed accordingly. K.I.S.S.