There are really two choices for you that you are mixing up since it doesn't make as much sense to use chlorine with Nature2. You can either use only chlorine, which most do using Dichlor-only but you can have the water last longer and be more consistent in disinfection by using Dichlor-then-bleach, OR you can use the Nature2 system with MPS with only shocking with chlorine once a week or so as needed. If you want to minimize the odor from halogens (bromine or chlorine), then Nature2 with MPS may work for you. Just follow the Nature2 manual.
Note that for some people MPS can be irritating though in a Nature2 system it's less likely (the silver ions in Nature2 break down the minor most irritating component in MPS products).