How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.
Even though you are using a personal account, choose an email address that looks professional. Your best bet is some variation on first initial, last name (e.g., [email protected].com) or first name, last name [email protected].com). Here's how to set up an email account just for your job search. Tips for Writing a Compelling Cover Letter. Get information on how to write a cover letter, including what to include in your cover letter, cover letter format, targeted cover letters, and cover letter samples and examples.