I think the mystery surrounding River is one of the things I really love about her! Usually, the supporting characters on Who are either people who've been around forever and are therefore well known (like the Master), or we get their whole life story when we meet them, like nearly every Companion -- it's not that the Companions are a total open book or that there's nothing to find out about them, but with Rose or Donna, Amy or Martha, we know what they are from the beginning: a shop girl who wants to see the universe, an accomplished doctor, a girl who's been waiting all her life for the Doctor to take her away, or whatever. We have no idea who or what River is, and I find that completely fascinating, especially as little hints about her are dropped.