Guy de Maupassant: "The Necklace" This classic is known to most English readers. In my opinion, it should be the first one you read. It is easy to find on the internet as well. Although originally written in French, the English version serves well as an easy text. If you require an English author, I would choose W. W. Jacobs' "The Monkey's Paw." Both are short, easy-to-read, and renown. The latter was published in 1902, but it solidly belongs to the 19th century in style and setting.

Try the authors O Henry and Edgar Allan Poe.

I wouldn't recommend a 19th century short story. Read a 20th or 21st century novel that has normal, conversational English in it.

The Adventures of Sherlock Holmes by Sir Arthur Conan Doyle