Use a business closing and sign your name. Above all, be professional. If the you’re sending a physical letter, print it out and sign it by hand. Otherwise, just typing your name will do.
Do graduate schools care if letters are confidential or not? In general, graduate programs prefer confidential letters. Admissions officials say that it displays more confidence on the part of the applicant if letters are "confidential" (meaning you, the applicant cannot see the letter). The Letter Service is required to indicate on the letter if it is confidential or non-confidential.