I have an involved cleaning process. I have a 2 tier K-Rims set up. My mashtun has threaded fittings, my BK is all tri-clamp.
The mashtun gets non-threaded parts taken off (the autosparge gets broken down except for the parts mounted to the kettle, otherwise, it's the false bottom that holds the BIAB bag and the dip tube) and hosed off. I'll break down the ball valve and clean that as well with just plain water.
I break the BK down and blow water out everything (fittings are removed and flushed and back flushed with water; I spray the CFC in both directions). The next day, I'll give everything a hot PBW soak. This is because my element inevitably gets a lot of hop residue stuck to it that comes off no problem after overnighting in PBW. I'll also flush and back flush the CFC (a Z-Chiller, so a convoluted star-shaped interior pipe) to avoid any chance of contamination. I'll typically rinse off everything once the kettle is dried (especially the riptide) and call it a day after that.
The initial rinse is to get most of the main debris off. the PBW gets the baked in/on crap off, and ideally prevents a hard-to-kill infection in the chiller.