While most are not legally binding, there may still be consequences for not complying with the agreed upon portions of the letter. A Letter of Intent is often seen like purchase or crowd-sourced orders, so they are often used to help secure funding or prove the value of the business. If the other party drops out or doesn't honor "in good faith" the letter, actual financial damage may be incurred to the company. In court, most often the judge will make decisions based on what implied intent is expressed in the letter. Sometimes there can be recourse if the parties do not follow through towards an actual legal agreement.
As with any professional correspondence, you don't want to seem too stiff or formal, like you're writing a letter from a Victorian template or a bad spam email asking someone to send money to a deposed prince overseas—but you also don't want to be too conversational. You're not in a dialogue yet, so it's important to treat this like a professional first interaction, and not like you're skipping several steps and asking to meet for coffee. The tone you're reaching for is, "You don't know me yet, but I'm interested in your company and want to tell you more about why."