Sure BSR is there to sell, and everything they show you need to buy. That is the most biased place to get information from, sorry.
Ammonia is not that toxic to marine critters, actually I dose ammonia on my 10gal tank that has no fish. That tank I just set up 4 months ago, again I put in salt water, added one rock from my large system and corals. Good to go.
No need to measure, ammonia, nitrite and once the tank is going for some time perhaps one needs to check nitrate. I have not check any in the last 6 months.
The corals and live rock OP has will consume ammonia.
Also OP has skimmer. There is no need to get additional filtration on the tank.
I run my tanks with skimmer and bit of GAC, no other filtration.
Pictures from my Reefer.
Couple pictures from my 10gal: