I've never done them on a stick. One of the awesome CC ladies here suggested hot gluing the stick and attaching it to the back of the bag and adding a piece of tape over it. Works awesome! They look great! (pic in my photos)
You'll find a variety of answers and I think it comes down to trying a few of the suggestions until you find the one that you like best.
I prefer to insert my sticks before I bake. Be sure the cookie is thicker than the stick (uh, guess how I figured THAT one out! 
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Once I insert the stick, I press down gently on the cookie, around the stick, to adhere the dough to the stick a bit better.
For bigger cookies, I'll (carefully) turn the cookie over to make sure the stick isn't exposed (if I pushed it in crooked). If I can see the stick, I'll take a bit of cookie dough and "bandaid" it over the exposed stick. Turn cookie back over and bake.
I don't have a problem with cookies spinning or sliding down the stick at all.
I like to insert the stick right after they come from the oven...that way they are in the cookie while it is cooling off and it stays on. Either a skewer or the wilton candy lollipop sticks...both work well for me. Of course the skewer is a skinnier stick andthe cookie doesn't have to be so thick, however if working with the wilton stick the cookie needs to be a lil thicker...
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