My DD (also a Miriam) and I started reading the RAinbow Magic just shortly after she turned 3. She's just turned 5 now and we are still reading them; but thankfully they are interspersed with a lot of other chapter books. I thought they were a decent introduction to the idea of a chapter book but so so so very formulaic and so so so very boring for me to read. The writing was - acceptable, I'd say, the plots identical, the goblins only a bit scary for a while but even DS who was just past 1 when we started reading them (he got to listen to all of them too!) wasn't very scared.
We've also burned through 40+ Magic Treehouse books, at DS's behest (he started asking for those when he was 2.5 as we had the first 30 thanks to their older cousin). Honestly, not sure I like them that much better. I'm not that fond of the interaction between Jack and Annie (the brother and sister featured in the books). I find the writing to be worse, and they are still very formulaic. They do offer the bonus of having lots of interesting historical and natural settings and fact that my kids enjoy though.
We are now reading an assortment of things; we've read the Sarah, Plain and Tall series which might seem too 'grown-up' in its themes, but they both enjoyed this and even deigned to watch the TV movie, a rarity since they are typically scared of movies. We've read Pippi Longstocking which is somewhat horrifying when read from a politically correct 2011 viewpoint but can be enjoyable if you're young. We've really enjoyed, and I highly recommend, the Canadian Flyer series. This is such an identical idea to the Magic Tree HOuse that I"m not entirely sure how the author hasn't been sued, but I find it so much better. Better written, plot lines less formulaic, bonus for being set in Canada. The interactions between the two main characters, friends Matt and Emily, are much more positive than the brother/sister interaction in MTH. We've also read The Moffatts, The All-of-a-Kind Family, and one of our most recent favourites has been the Anna Hibiscus books by Atinuke. These are great in that they are chapters books but each chapter is a stand-alone story and I also love the fact that they tell the story of a girl growing up in Africa, which is not something my kids would get to hear much about from other chapter books.
I could probably go on about other ones we've tried but I'll stop hear for now!