You have heard of L.M. Montgomery because of Anne of Green Gables, and I admit that the work everyone knows her for is perfectly fine; however, Anne's House of Dreams is the best book she ever wrote. It is, incidentally, the fifth book of the Anne series (which series L. M. Montgomery had not wanted to write even book two of, but had to because of popular demand). My theory is that maybe she had learned her craft well by the time she got to book five? I dunno. But it is truly her best, in my opinion and that of my old cello teacher, and you believe us, don't you?
For very nice romantic comedy fiction, you don't get much better than The Blue Castle, also by the esteemed Ms. Montgomery. I warn you that the romance doesn't start until literally half way through the book, but it is still very rewarding.
The Chosen, by Chaim Potok, had a profound influence on me when I was in high school, and even now I think about its themes a lot. Set in 1940's Brooklyn, it's about a friendship between an orthodox Jewish boy and an ultra-orthodox one. The ultra-orthodox kid is not super easy to be friends with, but the other kid's dad encourages the friendship, so he tries, but he doesn't really get why it's so important at the time. But who does, in high school? Or even later, sometimes. The time period this book covers includes the end of WWII and the holocaust, and a major question which crops up is about what it means to be "chosen" and how much pain can be involved with that. Along with some possibilities for redemption. I can't say that I have read almost all of Dr. Potok's other work, as I have with L.M. Montgomery's, but so far in my opinion The Chosen was his best (which is a little scary to me as an aspiring writer, since it was also his first).
A brief warning about Terry Pratchett: PLEASE beware of picking up stray British swear words that seem oh-so-innocent to you as an American but which really are deeply offensive in a number of principalities (which speak British English). But. Mr. Pratchett is really, really good at writing fiction which is: 1) deeply, profoundly silly; and 2) deeply profound. I may have higher needs for zaniness in my intellectual diet than other people do; I haven't done a comparative study; but I really do think that these books are lovely and worth trying.
Reaper Man-- perhaps my favorite Terry Pratchett of all time. About when Death (the anthropomorphic personification; the guy who is a skeleton and walks around with a scythe) looses his job.
Night Watch-- about good police work versus bad, and about-- oh, sheesh. I don't know how to describe it. Also about how to be true to what is true when it is for sure going to cost you your job and might just cost you your life. Also, just to drive the point home, it is profoundly silly, at least in spots.
The Tiffany Aching Series: Wee Free Men; A Hat Full of Sky; and Wintersmith. These combine a coming-of-age story with a very clear explication of what Relief Society is all about (if we were witches, living on Discworld). Also, as with the other Terry Pratchett books that I like so much, about death in one way or another.