Oil: The best way to prevent rust is to use an oil wipe, or a product like Gunslick's rust preventative. You want to oil all surfaces of the barrel and action (with the exception of the bore). This is pretty straightforward and if done on a daily basis, it's a great way to stop corrosion.
Muzzle Tape:** I always, always, always keep a strip of electrical tape wrapped around my barrel so I can keep the bore covered. You can shoot right through this (the air forced down the barrel blows out the tape before the bullet gets there). I've taken a lot of animals this way, and it in no way affects the accuracy of the bullet. It is important not to oil the bore, however, as this will often change the trajectory of your first shot.