Regarding the oil, we run Mobil 1 10w-50 in both the street cars that we build and the race cars that we race.
Like vbstang said your car comes with 5w-50 from the get go. We run 93 for our street cars. Our racers get 110 but I assume you are not interested in spending $10/gal
What you are hearing is most likely the diff. The Boss has stiffer bushings and less sound deadening so the sound from the diff carries through the body. I wouldn't be worried if its just a hum. If its a periodic rumble I would be a little more concerned =)