how do you handle your clean records?

Dropping a record on a hardwood floor should not be a problem. Just clean it and play. After all you wouldn't do it too often.
Also, take a record that is not valuable and intentionally drop it on the floor. Or, if you wish, I can do it for you and report what happened. I have a hard wood floor and can drop it from, say, five feet.
But I am carefull not to drop my Maxell Vertex cassettes that I regularly play. This could be unfortunate, though most likely even the cassette would survive the drop on the hardwood floor from three/four feet.

I also use Spin Clean. May I suggest buying an special attachment for a small shop-vac (covered with micro-fiber or velvet) and vacuum the water containing the dirt off the record. Better than simply wiping them dry. Easily available on eBay. Here's one that even comes with a spinner for the records. Other people sell just the attachment.

http://www.ebay.com/itm/Pocket-RCM-3D-printed-parts-Vaccum-clean-your-old-vinyl-with-your-own-Shop-V...

I certainly am more careful with my records now than in the past. I have at one time or another cleaned all of my records which count over 1200. When I play them, I have a light over them where I can see dust and fine hairs. Before turning the turntable on, I dust them off. About every fifth record I play I clean of the stylus.

I have abandoned all paper and plastic sleeves for soft fabric like sleeve that offers easy entry.

Well I have been working with the sliding the the record out of the sleeve and using one hand to hold and guide it routine. I can do it but I'm pretty clumsy at it or at least if feels very clumsy to me. I think like many of us I am much more careful with my albums now than I was when I first got a turntable. I have always had a turntable of some type. I think now I am finding my inner audiophile lol. I wish I could have and store 1200 plus albums! I have about 600 and I am working my way through them cleaning them all up. I have always used the brush method to keep fine dust and hairs off before playing, Stylus cleaning using a soft cut down paint brush. I am just very interested in keeping my record collection as pristine as I can. Next will be trying to figure out how to organize them so I can find what I am feeling lol. Thank you for the responses. 

When you are able, get yourself a VPI HW-16 LP cleaning machine. SO worth the money!