I clean the Ideal pretty much the same way. I either use wipes or I spray the toy cleaner onto the paper towel, wipe it on, then wipe it off with a dry paper towel. I was afraid of accidentally spraying toy cleaner somewhere it wasn't supposed to go, and it seems to work so far.
My answer to storage? For now, I leave it on my desk, where it charges when not in use. As far as the people I live with know, it's a back massager. I made a big deal of showing it to everyone when it came in and gushing about how I could use it on my OWN back when I had a flare-up, instead of having to beg someone to work on my back, or springing for a trip to the therapist. They know I'm discrete about making sure my toys are always out of site, so if it lives on my desk, it's not a toy. ^__^ Gotta love logic.
When it's time to actually take it off my desk and not have it within reach at a moment's notice, it actually fits quite well in the FYN Foot-Long, with its charger, with room to spare, strangely-shaped handle and all. Actually (I'm sitting here wiggling it around in the foot long in my lap) you could probably fit 2 Ideals, minus chargers, in here together. I don't have any attachments, but it looks like I could easily pack Ideal, charger, and an attachment in here together without much trouble.