The Death of Ivan Ilyich first.

Then if you have a background in 19th century history, War and Peace. The problem with W&P vs Anna Karenina is that W&P is not really a conventional story. It’s as much, or more, a polemic aimed at the duality of Russian society embodied in the twin battles of Austerlitz and Borodino. Austerlitz is a battle fought for vain glory and frivolities and Borodino is fought for a higher and more noble goal, to save Russia. Without that background knowledge it gets very confusing very quickly and the last 1/8 or so lacks impact.

AK is a much more conventional novel and probably an easier read.