I have a "brewery towel" that goes on the floor in front of wherever I'm working (stove, sink, under my bottles when bottling, etc). That is definitely a big help for me. I tend to be a bit of a klutz.
The right-sized colander on top of the kettle seems like a simple but excellent solution! Now I just need three hands, two to pull the bag out of the kettle, and one to insert the colander.You can put the bag in a large bowl while placing the strainer on the kettle. If your colander doesn't fit in a way it cant fall you can use two pieces of wood with strategic notches to keep them from moving across the top of the kettle.
I've had the colander and bag fall into the kettle. Big ol' mess.
I haven't really had a sticky floor from brewing since the late 90s. I used to brew with a guy who made a huge mess and always had to leave before clean-up. At that time, my solution was to cover the kitchen floor with newspaper.
My cleanliness problems were not so much related to the floor, but to the stove, the counter, and wort dripping off the counter. But some kind of towel, cloth, paper may not be a bad idea...