Hot water doesn't come out of faucet right away and makes banging noise when it does
Likely problems


Over-pressure from the street.  Solution is installing a pressure reducer just after the main shutoff.
Missing or leaking "water hammer arrestor", which is a vertical pipe with air in it or a tank with an air bladder, meant to soften sharp pressure changes.


Water temperature is not a likely candidate except at the extremes.  If you have a local tool library, or perhaps home store, they may loan out pressure gauges.