Toilet gushed water!
You may have a compromised seal between the toilet and the flange (where the toilet connects to your drain piping). This seal is usually done with a wax ring and can deform due to aggressive plunger-ing or movement of the toilet relative to the flange, such as when the bolts are loose and the toilet wobbles. 

When your drain is working normally, that seal does not need to do much - the drain pipe is wide open and the easiest place for water to flow is down that drain like we want.

However if the drain pipe is clogged, then liquid may build up against the seal until the clog is removed. This is where you'll see a leak along the floor and/or on the ceiling below. That would be consistent with your story. 

You should replace the wax ring. You will have to remove and reattach a toilet, so you're right that if you want to change the toilet this would be a good time to do so. Also, tile usually extends to just around the flange, so you usually don't need to match your existing toilet's footprint.