As others have said, water (and lots of it!) are your black tank's best friend.
We disagree with others in that we use the same TP in the RV as we do at home (Quilted Northern) and have never had a problem over the years (but, then again, I am a fanatic about LOTS of water in the black tank
Like Lou, I use the turbo rinse 15-20 min after EVERY black tank dump
We agree with others about NOT putting wet ones in the black tank (might as well be putting cloth in the tank!)
Never ever forget that your black and gray tanks are HOLDING tanks not septic systems! Remember this when emptying them as well: Let them hold as much as they can before you dump! (If we are out for a short weekend, I will use a hose and completely fill our black tank with water)
The chemicals you use to maintain your holding tanks are critical as well. Lou is correct, the GEO method is the best out there.
For us, we have found the best soap to use is Dawn Dishwashing Liquid. Amazing degreaser - the best out there IMHO.
All of us have our own home brew formulas for tank chemicals but the core ingredients are pretty much the same.
Dawn Dishwashing Liquid
(I also add 8OZ of RV-Digest-it to the above)
I make it in 2 Gallon lots, which is usually enough for the whole season. To dispense in the toilet, I got one of these:
Chemical Dispensing Systems for RV & Marine | Blue Streak LLC
This brew is tank agnostic BTW - I will put 4-6OZ in both my Galley & Gray water tanks after I dump them.
Hope this helps.