The most formal way of ending a letter is ‘Yours faithfully’ (when you don’t know the name of the person you are writing to). When you do know the name of the person (and it is a formal letter) you sign off ‘Sincerely’ or ‘Respectfully yours’.
‘Best regards’ and ‘Kind regards’ are less formal (they’re not used to end very formal letters).
If the letter is to a friend, it really depends on you and on how close the friendship is between you and your friend. You could sign off ‘Your friend’, ‘Take care’, ‘Wishing you the best’, ‘Be well’, ‘Cheers’ or ‘Take it easy’. If you want to be fun and creative, you can say ‘Over and out’, ‘Peace, love and unity’ or even ‘Tag! You’re it’. =)