If I can recall correctly...
According to the 'Silmarilion' (a book that I haven't read since I was 14. Mind you I am now 21, so my mind may be a bit rusty), I believe that the oldest character may be either Elrond or Saruman. I am leaning towards Saruman being the oldest though... if you don't include any of the trees or Saron.
And I know I just completely slaughtered their names.
By the Way, the Silmarilion is also a Tolkien book dealing with Middle Earth. It begins with the creation of the world until I believe the Hobbit. However, unless you really like history, I wouldn't recommend it. It'll bore you to tears and back again.