The correct expression to use in most contexts is ‘Well, thank you.’ This phrase is used to express gratitude in a polite and appreciative manner, often in response to a compliment or a kind gesture.
‘Why, thank you,’ on the other hand, is also correct but has a slightly different nuance. It can convey a sense of surprise or delight when receiving a compliment or kind words, almost acknowledging the unexpectedness of the praise.
So, your choice between the two expressions depends on the emotion you wish to convey. If you want to keep it straightforward and classy, ‘Well, thank you’ is a safe bet. If you want to add a touch of charm or surprise, ‘Why, thank you’ works well. Both are perfectly acceptable in conversation and can be used effectively depending on the situation.