I suspect that one's relationship with books and literature will in large part be, as you assess, significantly colored by ones childhood. The domestic situation you grow up is bound to shape your personality, so if you're used to being around books, and people who both read regularly, and who also read for you to let you discover the charms within, you'd be more likely to have a "natural" relationship with them later on in life.
My parents have told me that they made a point out of trying to get me and my two older siblings into reading at an early age, and this was something they mainly did through reading to us as children, and generally encouraging us to read, by recommending novels and so forth. It didn't hurt that they were both very enthusiastic about literature, and would often make small, interesting sidelines into novels while conversing on various subjects.
In our case, the result was that my brother and I have both become voracious readers, while my sister hasn't. She still reads the odd book now and then, and takes great pleasure in it, but it's just not what she wishes to focus on.
It should be noted that none of us were ever pushed into books in any ways, so my parents only really led us to the doorway, gave us some peeks at what was inside, and let us decide whether we were interested or not, without passing any judgement.
As I live in Norway, there's naturally going to be a different milieu in general from what others here think of as the norm, but generally speaking, I think most people are fairly positively inclined towards reading. They just aren't interested enough to do it very often, usually citing a lack of free time. Fair enough, really, as while I think reading can give you greater perspective and has been a great joy in my life, I don't expect everyone to get as much out of it. Different strokes and all that.
Most of the people I know who rarely - if ever - read, tend to also have grown up in bookless homes, only really being introduced to literature through school, which, in my opinion, unfortunately doesn't seem to work well in most cases. Even I was very negative towards reading novels at school, partly because I disliked the chosen literature, and undoubtedly also because I was generally negatively inclined towards anything the school wanted me to do.
I know plenty of people who recall how much they hated reading in school, when they're discussing why they never read novels.
This doesn't really answer your first question, but I guess I don't think there's any set age, but that it certainly won't hurt to show enthusiasm about it through your child's life. I find that my father's enthusiastim over books he read rubbed off on me and made me want to experience these things myself.
Sorry about the noisiness of this post; I seem to have caught a whiff of logorrhea today.
), but then my parents read to me every night. Phil's neice also loves reading and was introduced to it at a very early age. 
