For a genuine paper letter, it depends on whether it’s a piece of formal correspondence (letter of recommendation for a colleague, written complaint about a product), a cover letter for a manuscript submission, or a handwritten invitation or thank-you. Those might all get different closings. I still stay with “Sincerely” and “Very truly yours” for formal letters.
In e-mail I typically don’t use any except to family. It depends. At work it seems as if most people close e-mails with “Thanks,” but I don’t unless I intend to express gratitude for something. I mean someone will actually send out an announcement about a product release date, let’s say, with no actual or implied request or acknowledgment of any kind in it, and close it with “Thanks.” Isn’t that a bit silly?
I am always somewhat troubled by “best” because it doesn’t say best what.