And Then There Were None is a great Christie to start with! And it's an all-time mystery classic. It's without a doubt, far and away, my favourite of the books I've read by her. That book is also a "first" in a few ways, but I won't tell you what so as not to spoil anything.
ETA - And yes, you should be fine reading it. Her language is simple and pretty modern compared to some of her contemporaries. She may use a few more upper-crust early 20th century words, but that's good for you to learn from.
On the whole though it should be an easy read.