I usually put very little in the remarks section. If I want to make annotations that aren't really flying related, I'll do that in another journal or in my spreadsheet logbook.

I'd suggest trying to keep things professional if you're keeping a logbook for a career, simply because it's a legal record of your flying. But that's just my take... I'm pretty anal retentive about my logs.

If I had a flight where something was remarkable (such as a malfunction or other issue like a divert), I'd annotate that.

When I worked for the airlines, I kept a record of the crewmembers I flew with and the flight number. When I flight instructed, I kept a record of the student that I taught and the course/lesson number.

I'd suggest keeping it simple, but of course what you write is up to you. It's your logbook.