how do you handle your clean records?

Hold the record sleeve with your left hand and then tilt so the record slowly slides out if the sleeve.. You’re basically pouring it into your right hand.. Allow the record's edge to rest on your four fingers of your right hand and when the label comes out just use your right thumb to balance the record on the label.. Now you’re holding it kind of like you hold your pizza.. Easy stuff buddy.. Put it back the same way..

I think to must be an age thing…it drives me nuts to see somebody like Jimmy Fallon grabbing an LP by its edge and pulling it out of the sleeve when for about 50 years or so  I've been avoiding ever touching anything but the edge using the previously described "palm with fingers on the label" move. When Hippitty Hop DJs came around I thought damn…get yer fingers off that record! (old…I'm old..) Now Mister Fussy record cleaner man with anti static Mofi rice paper blah blah and WAY better gear says NO NO NO…I had a friend back in the day who for reasons I never understood would do a quick weirdly habitual forearm rub on his LPs before playing them…shocking!  Saw LPs made into bowls (really ugly bowls at that) at a craft show recently…tragic…I pointed out to the seller that it must be hard to play them at that point, and then wept silently (not really…but still).

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.