I'm fairly new to the area and still trying to get a handle on when the quietest times are during the week from London Bridge to HOP on Southern. Any suggestions?

You'll probably find the trains before 7am are quite quiet. I've also had occasion to be on a train in the early afternoon and they seem pretty quite.

But given that I have a job and a family, I find that the 17:19 train is a good choice to fit in with my life. I always get a seat, usually in the first class section (which is not really first class on our route).