Unfortunatly you will hear the words "you have to have this for your tank to survivr" when trying to set up your first aquarium. All you really have to have is salt mix, hydrometer/ refractometer, something for a filter (hang on back, dsb,skimmer, live rock), some live rock (not the recomended 2-4lbs per gallon), water movement, and decent lights and that is it. Many people were running great tanks before the advent of many of the expensive "must haves" and continue today.(garf is an example) The expensive equipment do make it easier and cover up mistakes quicker but it also turns away many people from the hobby.
SPS- If you want to keep these corals then you really almost need everything on the must have list. They are very fragile creatures that need almost immaculate water conditions with tons of water flow.
LPS- Some of these corals need water almost as clean as sps corals but you will pay put the nose for them when you can but the cheaper one that can handle an aquarium without all the equipment. some can't handle the high water flow or too bright of light making then great for smaller types of tanks (30 gl or less) that don't have a lot of room for equipment.
soft corals- Some people use xenias as a nutrient export in their tanks. They are the basic corals and are found in lagoons and other areas that are high in nutrients. some want high flow and light and others don't.
live rock- you don't need 2-4 lbs of rock per gallon , in fact amny people put too much rock in their tank that traps detritus and causes algea outbreaks.
4x-10x water flow- the more water flow that you have the more it keeps waste and other things in the water collum but you can do withou the high currents as long as you have a decent amount of movement throughout the tank. 2 unmodified max jet 600s in a 55 gl tank is adequate for anything but sps.
rodi - it helps but is trully not a must have item. Corals were kept and are continually kept with tap water tank but they do have to be cleaned more often.
3 THINGS THAT ARE A MUST
1 - patience
2- don't over feed
3- don't over populate
If you have different ideas then lets hear them.