I have it caseless at home, and I usually put my cheap TPU case on every time I leave the house. Most of the time it feels like useless bulk, but the few times I've dropped this phone, I've been thankful it's had a case and screen protector.
To me it just makes sense to invest maybe $3 in protecting a $300 device.
As for screen protectors, I use the cheapest money can buy (though I've been meaning to try a boxwave or steinheil). As long as you don't use a Zagg or similar, the screen feels smooth as ever, though the plastic scratches really easily on the smooth protectors.
If you read anything in this post, make it this: Gorilla glass is strong. It's hard to crack. Rub it with a key or pocket knife all day long, and it won't scratch.
But try taking your phone to the beach and putting it in your pocket with a few grains of sand. Say hello to the thousands of microscratches for me.
Glass can only be scratched by something harder than glass. Most metals you'll find, no matter how sharp or jagged, don't even approach the hardness of gorilla glass. But sand has some pretty hard stuff in it.
It's a personal choice, really. If you want to enjoy your device to its fullest potential, use it completely bare. But if you plan on selling it as "lightly used" for near full price when a new phone comes out, it's worth it to spend a few bucks on a case and a pack of protectors.