I have mostly blued rifles, but I have a 10/22 in stainless. I apply a coat of oil to my blued rifles after cleaning and put in the safe. My 10/22 gets wiped down with a silicone cloth. I feel that is adequete. It is also the rifle I shoot most frequently. It shoots about 600 rounds a month and I have had it for 13 years. It looks great.
The important part is getting all fingerprints and sweat off of stainless, unless you store it in a swamp, environmental moisture will not rust it.