A plunger is an indispensable tool which is required to dislodge clogs from tubs, sinks, showers, toilets and floor drains. The main idea behind using it is not to push the clog deeper but to vacuum it out.
A closet auger is designed for clearing clogs from toilets. It has a long cable made of steel which can remove any stubborn clogs. Lastly, a fire resistant cloth is must if you work near combustible surfaces and using an open flame propane torch. Also, do not forget to have a fire extinguisher handy.