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.
Anything that you'd use in an informal communication is inappropriate for a business letter. This includes slang, text_speak, emojis, and anything off_color or casual. If you're used to communicating mostly with friends, family, or even co_workers you've worked with for a long time, an appropriate closing for a business letter will probably feel pretty stilted at first. Don't worry about it – your colleague or business associate won't feel that way when he or she reads your correspondence. What seems unnatural to you will feel respectful and polite to the recipient.