Plenty mentioned on here about running the engines on load so wont go there..
Personally, I run up one engine, leave the engine bay open, check with torch for leaks, how the belts are running, coolent etc etc. Check for water pumping out the exhaust. Shut down and do the same on the other engine.
Running one engine at a time I can hear any noises or anomalies during start up..
I check gauges on both lower and upper helm.
We make a point to open close sea cocks when visiting the boat, and also spin the wheel turning the rudders. Maybe it makes a difference but there is time when the boat has sat for a while and maybe fouling could clog up around the steering