I'm a newbie as well. In general there are soft corals. Then hard corals - LPS and SPS corals. Soft corals are easiest but some can be invasive. Hard corals take more maintenance and you have to dose Ca, Mg and Alkalinity to maintain levels.
Again very general info but corals have specific requirements just as fish do.
LIGHTING, FLOW, PLACEMENT IN TANK, PLACEMENT IN RELATION TO OTHER CORALS (some corals sting each other /some do not)
Corals prefer certain light (low, medium or high), water flow (low, med. or high) , feeding (some get what they need from tank - fish poop, microplankton, some you have to feed etc.).
Some corals require special handling - like zoas and palys which have palyotoxin (a very potent toxin) - you should only handle them using gloves. You need someone to teach you how to handle these corals safely! If you have younger siblings in your house I would not put them in your tank at all.
Usually it is easier for a newbie to see what their tank 'likes' and focus on those corals. This can make things easier for you to maintain. So if your tank runs a little 'dirtier' soft corals and some LPS would handle that tank better. SPS corals prefer a 'cleaner' tank and die off quickly in less pristine conditions.
Your tank is so new that your water parameters can swing a lot. LPS and SPS don't like swings in pH, Alkalinity etc. So here is my advice:
KEEP A WEEKLY LOG OF WATER PARAMETERS
1- Keep a log of your water parameters. For future hard corals especially you need to know these levels: Calcium, Magnesium and Alkalinity
2- Also log Salinity, Nitrites, Nitrates, Ammonia, Phosphate and pH
Track those water parameters so you can see how your tanks runs. Take your time so you can track swings or see what your range your tank settles into over time. Then you can give R2R staff members your average readings so they can suggest corals that would do well in your tank.
Your tank sounds beautiful! You have some gorgeous fish stocked in it! Take time to look at corals in other tanks to see what appeals to you. You might hate quick spreading corals like "Green Star Polyp" or you may love them. Take time to see what you like, log parameters and then submit a list to R2R staff for advice!