I wash the funnel(s) with whatever cleaner is handy, Simple Green, Dawn, 409, etc. Wipe or air dry and store it in the drain pan which has also been washed clean and dried.
The funnel gets rinsed and dried again, immediately before it's next use. Between storage and use, it collects dust and who knows what else.
If a new oil container has been sitting around collecting dust, etc., I put it in the sink and rinse and dry it before opening. Otherwise, I just dry wipe it.