Don't use anything that might cause scratches, esp. in your plastic containers. Scratches like to hide bacteria and are difficult to sanitize.
So, here's what I do:
metal, such as boil kettles- after use, I just use regular dish soap and a rag, making sure I rinse very well after.
plastic, such as bucket fermenters or Better Bottles- after use, I use oxyclean (others use PBW). This I use as a warm water soak, then use a soft scrubby or sponge to clean. Don't use a regular carboy brush in BBs as it will scratch them. There is a special soft BB brush which is supposedly OK. Rinse very well. Then Starsan before using.
Glass, such as Carboys - after use, I use the oxyclean soak and a carboy brush. Rinse very well. Then Starsan before using.