The sign-off depends on the salutation. As a broad rule, if you addressed the letter to 'Dear Mr Debrett' the sign off is 'Yours sincerely'. If addressed to 'Dear Sir/Madam', then 'Yours faithfully' is correct.
If you don't know the name of the person to whom you are writing, start with 'Dear Sir/Madam' and end with 'Yours faithfully'. However, I would strongly urge you to find out the name of the HR manager. Individually addressed letters are obviously more personalised and, while it won't make a huge difference, will appear better than standardised ones.
EDIT (CLARIFICATION): The only traditionally appropriate way to start a letter to an unknown person is 'Dear Sir/Madam'.