Without wanting to come over as 'area-centric' I'd say US Billboard or UK 'official chart'  could be used as authority without discrimination, as each has been particularly well-used across the years as 'definitions of success'.
I would encourage references to other charts, with links if available; I see no reason success in another market should be considered as automatically 'less important'.
True international success would be reasonably well-reflected in many markets - though this would only really apply to English language material. Non-English songs have always struggled to find a market outside their language area, but I don't think, in the overall scheme of things, this should make a reference less valid.
As this SE site is an English language site, it would be reasonable to suggest that English language sources be given higher weight, but not at the expense of any other source, if that source is relevant to the question.
I would also say always cite your source, whatever chart you choose as your reference.
As always - questions will have more or less generally-acceptable answers based on the specificity of the question.
 The UK official chart has been through several incarnations, but the one the BBC used at that point in history would be my reference. This was the one always used by British Hit Singles & Albums (originally known as The Guinness Book of British Hit Singles and The Guinness Book of British Hit Albums)