Should You Read Hercule Poirot in Order?

There's no need to read the Poirot books in any particular order.

Should I read Agatha Christie in order?

Almost all of Agatha Christie's books are standalone, and can be read in any order. As you have noticed, some books do have minor references to earlier ones, but nothing major. If you are very averse to even the slightest spoilers, then you should read in publication order.

Which book of Agatha Christie should I read first?

Published almost exactly 100 years ago, The Mysterious Affair at Styles marked Agatha Christie's literary debut — which makes it a great starting point if you want to read her works in order. This is also the first time we meet Poirot, Christie's best-known character and a major part of her legacy.