Any food grade bucket will do. However, it is MUCH easier to bottle with a bottling bucket. The bottling bucket has a spigot and you hook your tubing up to the spigot and then a bottling wand on the end of the tubing controls the flow. No leaking, no oxygenating, no spills. Most people bottle with this set up.
To see if you have carbonation, there is really one one way- try it and see. Some people bottle a few bottles in soda bottles. Fill the bottle, and squeeze the air out and cap. When the bottle feels hard to the touch, it's probably carbonated. It won't be as hard as carbonated soda, but it will feel harder than before.