I would say it depends on what you need.
Thinner boards are better for signal integrity, but that is mostly for higher speed.
Thicker board are more rigid, which may be needed if you have few mechanical mounting and possibly big heavy connectors.
All big boards I have seen (like 300x500mm) were the standard 1.6mm. I only worked with 2.4mm boards where the thickness was mechanically wanted, yet was 100x100mm. It also had depth routing, it was like a big washer (just to be sure you get the right one:
https://en.wikipedia.org/wiki/Washer_(hardware)