Done about 15 or 20 rinks now, typically nothing to complicated.
We have a system that contains two brime pumps, VFD cooling tower and two compressors.
The brine pumps run anytime the system is active. Depends on the design of the system, sometimes its lead/lag between them. Others might run one pump if only a single compressor is running and more when additional compressor are required. Seen a few on VFDs as well controlling based on the brine return temp.
Cooling tower is normally controlling based on head pressure.
Compressors all depends on what you have. Many are single speed with a handful of unloaders. Typically these are controlling off brine return temp, with a low limit on the chiller leaving temp. Staging of the unloaders may be more about oil return than temp control. Some compressors also have a handful of solenoids keeping their oil levels in check. Typically see reciprocating compressors, though recently a few have been screws with slide valves.
Normally working with a national rink outfit, so they sort what the staging / loading sequence needs to be at startup and just make the controls dance to their tune. Every system is a bit unique in the compressor load up/down sequence. Those compressors typically have a wad of independent safeties mounted on them. You don't want them tripping in the middle of the night and open with wet ice to many times lol.
Only seen one rink that setback the setpoint at night. Most rink managers don't bother with this and set it manually depending on what kind of skating is going on that day.
The other things I would look out for are heated snowmelt pits that melt the shavings out of the Zamboni machine, pumps feeding the waste heat below the rink, domestic water pre-heat HX valves, pumps, high pressure blow offs, refer monitors, etc.