I bought some cheap cardboard drawer chests from one of the "storage" shops around here.

Thy are about 12' high and 8" wide and have 3 drawers.

Bottom drawer is for recently received razors, middle drawer is for ones that can be honed, top drawer is for razors that are shaving.

My routine:

Rinse the razor blade under the tap with just hot water, no cold, for 10 seconds. The gently blot it with a towel.

Then rinse out the cup and brush and put them away.

Then a few drops of oil on the razor, wipe of the excess, then into the top drawer.

No rust, no muss, no fuss. If I were cool, I would strop it and put it away, but since I strop before shaving, once the shave is done, I am ready to move on to somethinge else.