Pretty straight forward question.
I've seen people put it in a pitcher for between uses
I've seen people use a sanitizer solution
Do you find it gross to use it to wipe of the espresso from the drip tray?
This has been a discussion of late in our shop. You know; separating preference vs properness.
This is actually a place where Starbucks is right on the money - every place I've been since the 'Bux has not had as elegant a solution. There was a plastic tray with a little mild sanitizer solution in it slid under the espresso machine, with 2 towels in it. The towels were changed regularly, as was the solution. We would wring a towel out, wipe the steam wand, purge it, replace the towel in the tray, and slide the tray back under the machine, where nothing could fall or spray into it.
Anytime anyone questioned why we didn't use those towels for anything else, I suggested they lick the surface they wanted to wipe with the steam wand towel. If they weren't willing to do that, then they shouldn't be using the steam wand towel to wipe it (and yes, if it weren't for the heat, I'd be willing to lick the steam wands - that's how clean they should be).
We have a bench cloth (for wiping machine and the barista bench in front), a milk cloth (exclusively used for the steam wand) and a dry portafilter tea-towel which hangs from our dump box and is used for wiping our the PFs. They are regularly washed (especially the bench and wand cloths) and ne'er the twain shall meet. It's a big no-no to use them for anything other their designated use. Sometimes they get chucked through the steriliser as well to keep them spiffy. We tuck the bench cloth under the edge of our La San Marco, keeps it out of the way when not in use, but handy for a quick wipe and invisible to the customer.
Besides, if you use a milk cloth to wipe an espresso machine, any residual milk makes it all streaky and yuck.
The major issue of discussion was the exclusivity of the towel to the wand. I find it absolutely disgusting to use it to wipe of the drip tray. But I haven't been convincing.