It's really personal choice, and when you want to view your tank under certain lighting. In general, I think most here seem to have their main (both white and actinic) lights on for 8-12 hours. Mine are on 10 hours. The only issue with longer main light periods is the possibility of having algae issues. The LEDs can be 24 hours a day if you want, or they can be on only at night... it really doesn't matter.
I believe the "neon" type you're talking about is an actinic light? It looks very bluish? Here's my typical lighting schedule, just to give you an idea:
before 9:30am: all lights off
9:30am: actinic lights on
10:00am: actinic lights + main daylight (10k) lights on
8:00pm: daylight lights off, actinic lights still on
9:00pm: actinic lights off, LED