Fine hair relaxed is more likely to move naturally than coarse hair relaxed, but fine hair is also more likely to get damaged and break off than coarse. Do consider grow out, how you will handle having curly roots and straight lengths. If you keep relaxing or heat styling over the top of already relaxed hair you could end up with major damage.
Mostly I don't like obviously relaxed or dyed or flat ironed hair on men, it makes me think of the poseurs admiring themselves in the gym mirrors. Totally sexist I know since it doesn't freak me out on women (although makes me sad if they have fried their beautiful hair).