I suppose it didn't really touch on the deeper, darker, more graphic aspects until later. You feel for the characters, but there isn't really any really high-octane nightmare fuel or anything in the early books (in tvtropes-speak) until maybe until the David arc or slightly beyond. It walks the border between Children and Teens, but I'd say it started out as a children's series (I remember being hooked onto it when I was 10 or 11 or so).
It's a great, rather fun (if at times slightly scary) read for children. At the same time, reading and re-reading the series throughout my teenage years and coming back now as a 20 year old, I find out that almost every time, I catch on something that I would have missed out on when I was younger.
At 10, I was just generally having fun with all the animal descriptions and reading the book at face value (and learning how to write well, heh). I remember being hugely excited, though confused by some things. As a child, I didn't understand some of the more... ugly things (mature themes), like death, war, sacrifices, etc. They were just passing words, theories, if you will, with no real weight or impact. What I remember learning was about how everyone will have a different point of view. How differences in who you are don't make what you think any less important. How friends stick up for each other.
As a teenager, I looked a little deeper and saw the shades of grey, morality, sacrifices, the greater good, etc. In other words, stuff that I might have caught but didn't understand as a child, including war and related themes, which I linked back to what I caught as a child. And I think there's something in there for very age group and every reader, new or returning.
I think that RE stretching the boundaries, KA wrote the series across 6 years. Towards the end, I suppose she wanted to keep the same audience engaged in Animorphs.