Kegging time for beer under pressure or not?

You always want to purge out any O2 after transfer to the keg at least and putting some pressure in the keg ensures a tight seal on the lid. You will want to give yourself plenty of time to chill to the correct temperature for the pressure and carbonation you want. Going from 60F to serving temp at 30PSI the day before may yield suboptimal results.
I'd recommend starting the process 3 days before hand if you really have to try and do rapid carbonation. For someone new to kegging its really best to hold the beer at the right temperature and pressure for a week to get the perfect carbonation. I have been kegging for many years and I still get pretty variable results when I am forced to do it fast like that.

Always store under pressure. If you're storing for a long time before serving, and the keg will remain connected to gas, just set the reg at serving pressure. If you're going to disconnect it, you want to get it carbed up properly before disconnecting. In that case, you can either force carb and diconnect, or do a long slow carb and disconnect. In either case, keep the beer at serving temperature during carbonation. Once it's carbonated, you don't have to chill it until serving.