I'd second all of those suggestions but I find it strange that anyone would complete the 'start' checklist without verifying the radio and audio system following engine start-up. When doing the 'radio(s) on, frequency correct' part of my well-ingrained mental list, I always open the radio squelch by using the 'test' function (in the newer radios) or by backing off the manual squelch control in the old ones. So, don't wait until you suspect something - do it every time. Obviously, repeating the check if you suspect an in-flight problem is good, too. It won't eliminate all your potential radio issues but at least it clears a lot of the silly issues we can get into with volume settings, audio panel receive switches etc.
One other suggestion I'd make is to know how to configure and use your comms in the most minimal way. In many older Cessna installations for example, using the console mounted mic and overhead speaker bypasses some of the gear that people will have added over time. It's not elegant, but just might save your nerves.