My dad read the books as a child and still had them from all thos years ago. When I was about 3 or 4 he and my mum read The Hobbit to me and to be honest I think they soon started to regret it as I demanded to be read it every night. This, I believe, is why they didn't tell me about LotR til a few years later! I got into other books for a while and then reread The Hobbit for myself when I was 7 and continued on to LotR (which my parents finally told me about
).
So definitely the parent option!