Personal pronouns (like I, we, and you) are important in letters and memos. In such documents, it is perfectly appropriate to refer to yourself as I and to the reader as you. Be careful, however, when you use the pronoun we in a business letter that is written on company stationery, since it commits your company to what you have written. When stating your opinion, use I; when presenting company policy, use we.
Not only does this mean that you should focus on neutrality in your letter’s appearance (avoiding the use of colorful paper, brash logo designs, and artistic fonts), but it also means that you should employ a very low_key, unnuanced, and professional closing phrase. The best_case scenario is that the hiring manager, colleague, or connection won't even notice the closing.