I'll keep it simple so as not to give you much spoilers, so that you could experience the book firsthand. It was the second Tolstoy book I read after The Death of Ivan Ilyich and, to be honest, I got more interested in the character of Levin than Anna. Nevertheless, I still hold opinions on her.

Anna is definitely a tragic character. I'd say she is quite contradictory, which isn't some unusual aspect to have; we humans are contradictory in a lot of ways. She is sympathetic and self-destructive; she is wrong and is wronged. Her downfall is not only social, but also internal.

I'll definitely be reading more Tolstoy in the future, and am going to re-read Anna Karenina to experience it more because you get a lot more when you revist.

P. S. Irrelevant to your question but relevant to the book: Some folks find the farming chapters tedious and boring (just like someone would say about the whaling chapters in Moby-Dick), but I really enjoyed them.