I'd say Guangdong province.
First because "pin yin" (the Chinese phonetical transcription) is what is officially recognized, second because (sometimes) Guangdong refers to the province and Canton refers to the city (though normally Guangdong should be used for both).
This being said, your thread should better belong to the English Only section.
The thing is most of English speaking people I've talked to don't know the name Guangdong (They are from USA and Australia). And I want to precise the province name on that specific purpose: to make it clear for them to understand what I'm talking about.
Well, you are basically right for the way it is used now, though originally Canton (city) = Guangdong, Guangzhou being written with a different (zhou) character .
But discussing Chinese would be off-topic here.