First battery charge on new tablet?
there is no significant difference between charging it while it's turned off or not.
Modern Li-Ion and Li-Po batteries which are built into tablets and phones nowadays can handle any kind of charging very well. The only thing that should be avoided is a complete discharge as it degrades the battery MUCH faster (aka it loses capacity). With discharging I mean draining it to 0% and leaving it for some days/weeks alone.

TL;DR: Just use your device as you want and avoid being on 0% battery for a long time.