Should quest mods be installed ASAP?

I would say that install all the mods before starting a new game, except the ones who specifically say that you should install them at different point, like that Helgan reborn. Check out the respective mod readme and/or instruction files to ensure functionality. It is always a slight gamble if the mod functions correctly. Some mods may not even function if you do not start a new game to begin with them.

It's usually safest to install mods before you start playing on your character, but it's generally safe to install mods mid-playthrough as well. It will highly depend on the mod itself and reading the mod author's installation instructions is always important. Try to follow them.

In some cases, you cannot access a required piece of vanilla content due to a mod overwriting it, so you'll need to do that first in vanilla. But cases like that are rare and often caused by poor mod design.