Either Black or black is fine. I've only considered myself to be black (no capitalization), but I wouldn't find it offensive either way. I don't find African-American to be offensive but it can get confusing. I have non-black friends from Africa - who would be considered Asian or white by ancestry and appearance - who genuinely wanted to know how I could be African-American but they couldn't. I have no ties to Africa (other than historic genetic ones) and they were literally African-American. Black or black seems to better encompass what historically negro, colored, Afro-American and African-American intended.