I agree with you on both counts. Both Snow and LStark have gotten more interesting. I think its an indication of good direction that a lot of characters I wasn't initially excited about are developing into characters I like. Lots of kids in the movie with significant roles and they are doing a good job with them.
I had hoped to get my wife interested, but its been relatively slow developing and I am not sure I can get her into it. Four episodes in and not a ton has actually happened yet from a TV series perspective. I think its exceeded my expectations and is really amazing looking, with solid character development. I dig the story line, so I am in for the series.
Since you have not read the books, I think the only insight you will be lacking that might make it confusing is that the world in these stories moves on a different seasonal pace. The days are essentially the same during "Summer" i.e. it gets dark at night, light during the day -- although it is never discussed directly in the books to my knowledge. It is clear that the two main seasons, Winter and Summer, are variable in length and can last for years. It has never gotten to Winter in the books, but the constant suggestion is that there is no daylight during Winter. There has also been no direct discussion of magic in the books, but I suspect that magic ebbs and flows on a similarly long frame of reference calendar. There used to be some a long time ago, but there isn't really any in the current story time.