Any advice or words of wisdom for toilet leaking through floor/ceiling?
It sounds and looks like the wax seal has failed. The good news is this repair is not hard. The bad news it is a "dirty job" . 

Step 1 get a new wax seal at a plumbing or big box store just a couple of bucks. I like the ones with a urathane center they are a bit more expensive but 5 bucks is not a big deal. Also pick up some disposable gloves and a narrow putty knife (makes removing the old wax easier)

Step 2 turn the water to the toilet off and flush you want to empty the tank. If you have a wet vacuum suck the small amount left in the tank out and also drain the bowl, if no wet vacuum a small towel can be used to soak up the water and squeeze out down another drain. 

Step 3 remove the supply line to the toilet. 
Step 4 remove the 2 bolts at the floor, 1 on each side. 

Step 5 lift the entire unit by the base not the tankand lay on its side.
Step 6 clean the old wax seal off the bottom of The stool and the top of the toilet flange (the plumbing at floor level). Make sure to remove the rubber cone.  

Step 7 take new seal and mold it to the bottom of the stool. 

Step 8 this is the toughest part, pick up the stool by the base and position it over the bolts and lower it then press down, once the bolts are through I usually sit on it to help squash the seal a bit.
Step 9 install the washers and nuts tighten both sides a few turns each until snug, sit on the stool and see if it is loose if it is tighten a little more and check again (a stool that wobbles will shorten the seal life).
Step 10 replace the water line and turn on. 
Once the tank fills flush and verify everything is working with no leaks.
Now just to clean up and dispose of the old wax ring &amp; gloves and realize you just saved a bunch of $.