I think relays are too switch too slowly for zero crossing to matter. For triacs though, switching on at the zero crossing reduces noise. Switching off would also reduce noise but for triacs this is a non-issue because of the way peculiar triacs work. Once turned on, they stay on. The only way they can turn off is if power is cut externally (ie. the zero crossing). So triacs only turn off if the control signal is removed when a zero crossing happens. THis is why they aren't used with DC. You can turn it on, but not off unless you have a switch somewhere else that can actually break the current flow.
For relays it definately would reduce noise and prolong relay life by reducing sparking when the contacts open. It would also reduce noise when the contacts close just like the triac.But as I said, I think relays are too slow to reliably switch on the zero crossing.
Incidentally for a transformer turning on at the zero crossing is the worst time to turn it on. It basically causes a massive inrush current spike on startup which might saturate and overheat the transformer because of the way transformer magnetizing or leakage currents work. I don't fully understand it myself.
I'd fuse something connected to the mains because if something goes wrong (like a short) you might destroy your board because it might melt or light on fire and you would instead trip the breaker.