Different cleaners and sanitizers need to be used for different jobs and situations. It is REALLY IMPORTANT you familiarize yourself with the below:
Removing brown spots or dark staining (especially see on lids):
These spots can be cleaned very nicely using Bar Keeper's Friend. This is an oxalic acid. But BE VERY CAREFUL NOT TO USE ON THE ETCHED GALLON MARKINGS OR LOGO because those etchings use an oxidization process as well and Bar Keeper's Friend will fade them rapidly especially if wiped with a rag, etc. Bar Keeper's Friend should ONLY be used in a very localized and tactical fashion on any stubborn lid stains that are bugging you, but again just be careful not to use around gallon markings or logo etchings.
Removing krausen deposits:
Use PBW or similar caustics as these are good at removing proteins left behind after fermentation. Best to clean your fermenters ASAP after you rack your beer out of them. If there is any stubbornness, then just let soak a bit and you should be good!
Removing manufacturing residues:
Caustics (like PBW) don't deal with oils and residues from manufacturing very effectively, but TSP (non-chlorinated only!) does a great job at cutting residues, oils, grease, polishing waxes, that kind of stuff. If you don't have TSP available, then a good detergent is fine. Use a soft cloth only and don't use abrasive pads or cloths. Also prior to passivation you should use TSP to clean first
Removing white powdery/calcium looking deposits:
These types of deposits are typically calcium which has precipitated out of solution during cleaning if your water is really hard. If this happens, no worries - just use an extra concentrated solution of StanSan (4 x the usual ratio of solution to water) and this will readily dissolve the calcium back into the soak solution and you'll be good as new!