When I am asked which corals are the easiest for beginners, I usually nominate the fox coral, Nemenzophyllia turbida; cabbage coral, Sinularia brassica; bubble coral, Plerogyra and Physogyra; and the ubiquitous Discosoma 'shrooms'. All of these are very hardy to situations that novices are likely to encounter, and do fine when the nitrate and dissolved organics levels, are as expected in a 'fish only' aquarium, as opposed to what people expect of a 'true' reef tank. Corals are not necessarily more difficult to care for than are fishes, but most require correct lighting, and all need sufficient flow to bring these sessile creatures food, and let them void their wastes. None of the above corals are extremely demanding of either parameter.
Different corals extract different resources from the ambient water, at different rates as befits their biology. Thus fast growing colonial and clonal species, may demand or prefer the dosing of additives to their water. If and when the aquarist feels competent to handle dosings, he or she may also consider Zoanthus or 'zoas', which appreciate iodine, or despite misinformation, the long polyp or pom pom morphs of Goniopora, which are dependant upon magnesium.
Needless to say, there is less need for dosing additives, when the water volume is large relative to the biomass of corals. Some common sense is as useful as is knowledge of coral biology. But it is is worth bearing in mind where corals come from on the reef and nearby, the phenomenon called zonation. Intertidal corals, and those from turbid lagoons, are naturally the easiest to care for, because these environments experience variations in temperature, salinity, and wavelengths of light, the latter being due to turbidity - it pays to study corals, before choosing corals.
Where there is lower flow on the reef, there are also more dissolved organics, available as a nutrient supply in the water. This is in fact beneficial to those coral species that are adapted to these environments, and they do not fare so well in crystal clear, well filtered and excessively skimmed water. Indeed it is helpful in the aquarium, when replicating such biotopes and microhabitats, to calculate the bioload of fishes, as it would in a fish only system. The flow should gently ruffle the corals without too much disturbance, and the lighting need not be too intense per tank depth, though its spectrum should of course lean to blue and be relatively low on red.