Should I put caulk/silicone at base of toilet on hardwood floors?
I think you're confusing the terms "caulk" and "silicone" for the colors "white" and "clear".  A lot of caulks are made from silicone rubber, and they can be white or clear (or other colors).

To answer your question, I would use a clear caulk around the base of the toilet as it will look better next to the wood.  I've always used caulk because it prevents any, uh, splashes, from running under the toilet where they'd be hard to clean up.  Leave a small gap at the back of the toilet so that if you do have leaks, they'll have somewhere to drain to and you'll be able to tell.