I can't decide which would be better, popsicle, sucker.....Can you help me?

Depends. What are you using it for?

k hmmm, interesting,
let's see here, I would use the popsicle sticks if I did have to put it into frosting or cake where moisture would be an issue. If moisture isn't an issue i would go ahead and use the sucker sticks.

I have edited the subject line. I want to make cookie on a stick.

Dowel rods or bamboo skewers if you are making them large-ish.

I use the paper sticks that Wilton makes. You just put them in the cookie and bake them - stick and all!