Is there a list of common mods or popular gen parts that people tend to start with?
It varies from level to level of accuracy and model. Quite frankly it's almost impossible to list out every mod for every watch, and people's tastes vary on what they can tolerate. Most "gen" part mods are diminishing in returns quite frankly. Everything here is also my opinion.
I only discuss Rolex here, since Rolex replicas are at the level where they can take gen parts easily.
Most common mods are a swap for gen crystal.
Then generally dial/hands for the white gold nature of the markers and the hands.
If you've done all that might as well get a date wheel.
But then after that it's all up to you. I mean you can swap the bezel insert, crown, etc, Personal preference.
In my eyes :
For Submariner
Gen Crystal > Dial/Hands/Datewheel Overlay > Bezel Insert -> others
For the Datejust, see it's different, it would be
Gen Crystal > White Gold Bezel > Dial/Hands/Datewheel Overlay -> others
You can also see why I say in the other post it's a personal thing. Some people may compare the gen and rep insert and think that $1500 for a gen bezel insert isn't worth it, while some think otherwise. Some people may want to swap the date wheel but are fine with the dial. etc. Which is why I told you to get the replica in hand and decide what "bothers" you about the replica before deciding to mod it.
At this stage in the replica game, most Rolex replicas are already good enough out of the box, use a simple crystal swap and you're done. Enjoy it.