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.
Since your signature is likely to be difficult to read, type your name down a couple of lines so that your reader knows who is writing to them. Enclosures: (Below signature block) If you have included any further material _ a business card, a brochure, a price sheet, whatever _ list the number of items and describe each. Finally, proofread, proofread, and proofread again. While a friend might excuse even the worst spelling and grammar, a business letter is often your first (and maybe only) chance to make an impression _ it needs to be impeccable.