What kind of caulk to use in order to caulk the toilet to the floor?
It is best NOT to caulk this location.  Caulking this location can lead to moisture from a leaking toilet getting trapped under the toilet and creating a haven for mold (and/or rot, should there be wood in the area).

In your case remove the toilet, and replace the wax seal (or use one of many rubberized "no wax" products, which claim to be better.

If you do caulk the location, I recommend leaving a gap at some point, perhaps in the back of the toilet, to allow some air circulation. I prefer a quality latex caulk to silicon, as the silicon never seems to stick all that long.