Welcome to reef keeping and to Reef2Reef!
There's stuff that builds up in the water (hydrophillic Dissolved Organic Carbon) that is best removed (and may only be removed) by water changes. Unfortubnately this si something we can't test for but research shows it can be very detrimental to corals. How fast it builds up in a system depends a great deal on the balance between corals, cryptic sponges, algae, fish and most importantly all the microbial stuff. In my maintenance business I've had very good long term success (as in decades) using small 5% - 10% weekly water chagnes. Initially that's what I'd suggest. Long term once you've learned alot more about your animals and get a feel for how your system is running you may decide some other water change regimen is sufficient. Just keep in mind corals can look ok but can actually be very sick. And I'd point out here many of your animals should live decades if properly cared for.
As far as testing unfortunately we can't test for all the forms of the three major nuttreints, Carbon, Nitrogen and Phosphorus. Our tests are limited to basicely the inorganic forms of these and there's a lot going on with the orgainic and particualte we are unable to test for. Sadly, one consequence is you will find very differing and conflicting opinions on what you should do. But I would echo the above recomendation to test frequently at first as it will help you get a feel for what's happening in your system as it sycles then goes through the maturing process (~8 - 12 months) and beyond.
These may be a data bomb and I'd suggest rewatching them a few times over several weeks but here's some really good videos expalining what all is happening in reef systems:
"Coral Reefs in the Microbial Seas" This video compliments Rohwer's book of the same title (Paper back is ~$20, Kindle is ~$10), both deal with the conflicting roles of the different types of DOC in reef ecosystems. While there is overlap bewteen his book and the video both have information not covered by the other and together give a broader view of the complex relationships found in reef ecosystems