Does closing my cover-letter with salutations or closing phrases like sincerely yours or yours truly make it look like an email? If so, how best to close the letter?
Assuming you are writing a full cover letter ie a direct pitch as to why you meet their requirements.
The formal way in English is:
"Yours sincerely" when you know the person you are addressing, "Yours faithfully" when you are starting your letter with Dear Sir/Madam, etc
If you mean just a five to ten line email with a word or pdf attachment - you could use the above or Just "Best Regards"