Should I replace my toilet's wax ring when I see moisture around the base?
Before you start verify that the supply line or tank isn't leaking , dripping down the back of the bowl and flowing around the base. If that looks good I would pull up the toilet and at the least replace the wax ring. I say at the least because most times the bolts get loose for a reason. It may be a cracked flange, broken bolt, rotted floor etc.  You have no idea how long it has been leaking before you noticed it. By taking up the toilet you can examine the flange, the floor, the subfloor and the bottom of the toilet to determine the cause of the leak. This will allow repairs to be done in the earliest stage. It will be easier to repair the flange if that is the issue then to wait and have to replace a piece of rotted subfloor.