The HW45 frame is aircraft aluminum so it won't rust. Mine is 6 years old now and still looks like new. Occasionally, I wipe off the frame with a soft towel with nothing on it. I use a cotton swab or patch to apply a bit of oil to the exterior of the metal compression tube but it never gets touched so application is not often. The exterior of the barrel gets the same occasional treatment.
I never store airguns or firearms in cases.
Cheers,
Todd