Its an easy thing to get tripped up on but first- Congrats on your new tub.
Copper and Iron are the minerals that cause staining and corrosion. Mineral cartridges, such as Nature II or Spa Frog, use silver (and an extremely low amount at that) as the active ingredient. Thus- Mineral removers (aka sequestering agents) are designed to detect and surround copper and iron so that they are picked up by your filter and can be removed once your filters are cleaned.
Additionally- Mineral systems have something else besides the mineral stick that sanitizes. Nature II, for instance, uses the stick as what I deem the "passive" sanitizer (when your water is sitting there w/o being used). Then there is an "active" sanitizer, which would be Potassium Peroxymonopersulfate (MPS, or Spa Shock). That is used when you get in the water and contaminants such as dead skin cells, sweat, lotions, etc. are introduced from your body.
Regardless- A sanitizer is only 1/3 of the equation. pH and Alkalinity are just as important. High pH/alkalinity cause metals to be pulled from their sources (how your heater corrodes and how your jets fail) whereas low pH/alkalinity cause metals to deposit (staining and scaling). Additionally- imbalance of pH/alkalinity cause whatever sanitizer you are using to not work at its best capacity.
Chlorine, Bromine and Mineral Sticks are the 3 most common sanitizers on the market. Really all 3 are fine- I've used all 3 and sell all 3 and I don't care either way. There are pros and cons to all 3 so I just advise on that and let my clients make the final decision. Lots of people push Spa Frog/Nature II as it is the most expensive and they can get you on the come-back. I dont really care.
Just be sure to test your water regularly and keep things in balance at all times. The first fill (4 months) are always the worst. Once you get into a routine you become predictable. Thus your water becomes predictable. Thus your treatment becomes predictable. Thus your headaches go away.
Make sense? Hope this helps. Good luck moving forward.
[edit: syntax correction]