Which of the three phrases in the concluding phrase is most appropriate when sending a work-related email?
Could the three be ranked in terms of their overall level of formality?
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As with most things, it depends on the context. Any of your three options are essentially short for the more complete thought, "I send this letter with my regards." You have to ask yourself, does "sending regards" actually make sense in the context of your business position? One would typically use this phrase for long-distance communication, as they are "sending" their emotional investment in which they can not personally deliver themselves (in a metaphorical sense), and having it travel along with the mail. If you are talking about an office environment, it makes a bit less sense.
I recommend using some form of "Thank you" instead, as one is usually asking for the help of coworkers, managers, customers, or such; at the very least, you are asking for their time and effort in reading your message. "Thank you," "Thanks," "Greatly Appreciated," and "As Always, Thanks Again" are all reasonable options.
Entirely up to you! "Regards" is the most formal and "Best regards" the least formal. With Regards somewhere in between.