American here, similar style, I just use 'Thanks' instead of Best. They're similar in just being short and kind and impersonal. I think both are about perfect. Anything less seems unprofessional, anything more sticks out like a sore thumb.
Usually just my first name unless it's formal and introductory, as my email will come from First Last as the sender already.
Cheers is fine in the US I think, but I at least assume the speaker is British or Aussie. If I know they're American, it comes across a little pretentious or inauthentic IMO...same as when Americans say 'the states.' Makes me roll my eyes but not like day ruining or relationship affecting.