We have always used whatever TP we have in our house, we buy the big box of POM 2-ply from Samsclub. Everybody has their methods and their reasoning behind them, similar to what chemical or concoction they use for their black tanks, for either issue the solution is using plenty of water.
When RVing in the summer we use the cheapest deodorizing chemical from Walmart without regard to brand, rest of the year just H2O. We backflush every time we dump, at least once a year we use a tank wand to get the nitty gritty off the sides and bottom of tank, not much TP is stuck inside.