You can also include links to online portfolios, if appropriate, or a link to your professional social media account such as LinkedIn or Twitter. You don't want to make this section too cluttered, however, so restrict yourself to the most relevant information. Here's how to set up an email signature, along with more advice on what to include in it and what to leave off.
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.