The very first thing to do is completely strip the gun down and clean all parts with Hoppes 9 or some other solvent. You MUST clean off all the packing grease off EVERY part. This includes - IMHO - even the spring inside the recoil spring tube.
To remove the spring inside the spring recoil tube you'll need to apply heat to the bolt head as it has lock-tight applied at the factory (a Bic lighter ought to do the trick; just need enough heat to loosen the lock-tight). You'll want to disassemble and clean this part because of any packing grease but also because you will eventually get dirt inside the tube and it will interfere with the operation of the inertia recoil. Take it apart now and you'll be good to go for future cleaning when warranted.
Then run a 100 rounds or so through the gun. Light trap loads will be fine.
Regards oiling: use a synthetic like FP-10. If you're shooting in below freezing temps, I'd run the gun dry or with very very little oil under the bolt assembly (very little). If running in warmer temps, apply very little oil on bolt rails and under bolt assembly.
Bottomline: freezing temps and below start to slow the action of the inertia down, so use very very little, and remember that oil acts as a dirt and dust attractor, again, another reason for using oil sparingly.
Good luck!
The M2 is a great shottie.