There are no hard and fast rules about what greetings (salutations) to use in email. If you want to be polite and formal in English, then you should say something like:
Dear Mr. Smith:
Dear Ms. Jones:
Dear Dr. Jekyll:
Dear Prof. Einstein:
If you want to be polite and informal, replace the colon (:) with a comma:
Dear Mr. Smith,
etc.
When authors send me a manuscript, regardless what salutation they use to address me, I always start off this way:
Hi, Dr Jiang,
Hi, Prof Jou,
(Almost all my clients are Taiwanese doctors and medical school professors).
When I write to my friends, I always start of the same way:
Hi, Tam,
Hi, Kathy,
This is just a stylistic choice, a personal preference.
For business letters other than my editing, however, I always use the polite formal style in the first examples.
There is no definitive answer to your question, just a recommendation that for serious and important business letters (anything not to a friend or a penpal, and anything not informal), that you use the polite formal or polite informal style. You can find lots of choices in handbooks about how to write letters in English. Be advised, however, that different brands of English prefer different styles. The one that's best is the one you feel most comfortable with and the one that you think works best for any particular letter.
The more formal and more polite your initial salutation, the more emotional distance you put between yourself and the person you're writing to.
For friends and otherwise informal emails, the same rule of thumb applies: The one that's best is the one you feel most comfortable with and the one that you think works best for any particular letter.
Everyone has a different idea about what's good.
You might consider simply sincerely. Sincerely yours does sound a bit off to me for professional correspondence; I might indeed be sincere, but it's doubtful I'm theirs. Regards has always sounded a bit stiff to me, but I wouldn't look twice at it; it's common enough. Even sincerely sounds strange to me for email; I would certainly recommend it for a handwritten letter, though.
You've got to consider the difference in levels of formality between email and letters. For a letter, this would look perfectly fine to me:
Dear Jane,
[body of letter]
Sincerely,
[name]
But in an email we're generally much less formal, both in closing and opening. I'd take off the dear and use something less formal for the closing. For example:
Jane,
[body of email]
Thanks,
[name]
But plenty of people do use regards, and no one is going to think it strange if you do. Sometimes emails begin with hi as well. There's really nothing wrong with always using the same closing, either, so if regards works for you, use it! In fact I think most people do use the same closing most of the time. Considering my own email habits, I think I tend to do one of three things: 1) If I'm just sending along information, I don't use a closing at all; I simply end with my name. 2) If I'm requesting something of someone, or thanking them for something they've already done, I'll use thanks. 3) If I've written a significantly longer-than-usual email or am requesting significant effort on the recipient's part, I might end with thank you for your time. In a letter, I pretty much always use sincerely. In my experience, most people do. But email varies quite widely, so I wouldn't worry about this too much!
Best Answer
"Hi John and Mary" is more polite than "John/Mary" but that is probably not the source of the feedback that your emails are bossy. It might have more to do with how you phrase your requests, especially to other managers and peers.
"Hi John/Mary, I haven't received your comments yet on the report. Please get your comments to me by the end of the day. Thank you." = sounds bossy.
"Hi John and Mary, just a reminder that the report is due tomorrow and I need to include everyone's comments - will you be able to get your comments to me by the end of the day? Thanks so much!" = sounds nicer.
Be careful about ending sentences with periods in your emails. For some reason, many people (especially younger people who grew up texting) will think you are angry.