That shotgun shipped with oil, not grease. Grease has a 'thickness' to it that is real - which theoretically is not good for the hinge of the gun. Further, there are parts designed to move quickly and the viscosity of grease can hinder this movement.
Any lubricant can and will attract dust/dirt - and grease is much worse than oil for this. Most will wipe off all lubricant when they clean the gun, and re-lube when finished.
If you bought the gun new, it should have come with oil and instructions where to oil. If not, you can download the instruction manual from the Beretta website. Apply whatever lubrication you are going to use sparingly. I use oil in my Berettas. Enjoy your new acquisition.
I've used shooters choice red synthetic in the past, in a pinch I've used Mobil 1 out of my grease gun, but lately I have been using slip 2000 EWG (extreme weapon grease). For o/u shotguns grease is the only way to go in my opinion.
My 682's get grease. Not sure it matters that much what flavor. I've used Red and Tacky, Super Lube, Gun Glide, and wheel bearing grease all with good results. Put it on before you shoot and wipe it off after.
Grease is just the medium, it holds the oil. It will turn to a liquid when it gets hot (the gun)., and back to a more solid form when it cools down. In the warmer months I use a heavier grease, a lighter one for the colder months. It doesn't matter as long as use something!! Don't go dry!!