Not much difference: my corals are easier, than my fish (messy eaters).
Additional tests - KH, Ca; Magnesium and phosphates are optional, but could be sometimes useful, if you have unexplainable pH and algae growth.
Most expenses, beside corals, will be live rock and lights, with bulbs exchanged every 6 months.
Depending on what kind of corals you like, you may need a lot of lights (400W) and/or very good filtration and skimming. Some common corals will do good with less light.
Feeding corals: a lot of information is on the web. The general idea for a corals with visible mouthes is to put reasonable sized for this mouth food (or a few smaller pieces) onto the mouth or into tentacles, if there are ones. Using tweezers, feeding prong (acrylic atick) or pipette (or turkey baster).
Or, if you feed the whole tank, put frozen cubes in the area of high flow, and some corals will pick what they need. Just keep water quality reasonably good (cleaning, water changes - you know).
Food: the same as for a fish - chopped seafood for a large mouthes, ocean plankton - for a medium, mysis and brine shrimp - for the most of corals, dried Cyclop-eeze for a small mouthes (800 micron size), even less - ZoPlan, smaller than that require special care.
If you didn't know what you like, you may see threads with names like Idol tank, or general web search for a Tank of the month, and see what you prefer - SPS and clams tank require totally different setup (high light, cleanest water, finest food ~50 mk, healy filtration and skimming). If mixed reef is OK - it's much easier, nothing special. Check, what corals you would like to have at the sites, like peteducation.com/corals (by type), then check requirements for each of them. This will give the general idea.
LPS are frequently stinging - leave some space between them and other corals, the soft corals in many cases expel chemical compounds - run carbon or/and skimming.
Non-photosynthetic corals don't require light and are sometimes nocturnal, but they should be very well fed, and this means water changes, or/and heavy filtration, skimming and refugium or denitrator. It's a heavy burden.
Step-by-step, one coral after another, when you know name of the wanted or bought coral - it's more that easy to get immediate results by search.
Really, reef-keeping is not hard as it seems to be. Keep a good-looking tank - is another matter. Aquascaping, color gamma and such.