Katharine Hepburn was among the top candidates for Scarlett, even though the public openly questioned if she was right for the part. It was not a question if she would be able to carry the part acting-wise, rather, as Selznick put it in his letter to D. O'Shea in November 1938: "...I think Hepburn has two strikes against her - first, the unquestionable and very wide - spread intense public dislike of her at the moment*, and second, the fact that she is yet to demonstrate that she possesses the sex qualities which are probably the most important of all the many requisites of Scarlett..."
(*In 1938 Katharine Hepburn, along with many other studio stars was named a "box-office poison".) 
There was the so-called "Hepburn incident" in the fall of 1938. The vice-president of the New York Herald Tribune, announced that Katharine was Margaret Mitchell's choice for Scarlett. She based it on an interview that she had conducted with Ms. Mitchell earlier, but twisted Ms. Mitchell's answers. Later on the misunderstanding was cleared up. But until the final casting she remained one of the strongest candidates.

Joan was first scheduled to do a reading for the role of Scarlett, but she asked for a test and Selznick agreed. She remained among the final four candidates, who were tested in the last days of December 1938. Joan's tests were made on Monday, December 19th, 1938 and it was a scene with Scarlett and Mammy preparing for the barbecue.

Until the final decision, Jean was among the three at first, and then four actresses that tested for the role. As to why Jean was considered to such an extent, not even fitting the physical description of Scarlett is debatable. Rumor has it, that years earlier Jean was David Selznick's sweetheart and the tests were made out of sentiment. 
Jean's test was made on Saturday, December 17th, 1938 and it was a scene with Scarlett preparing for the BBQ. As David reported in a letter to his wife in New York: "George is busily engaged on the Scarlett tests. All day today with Jean Arthur, who has been no end of trouble (I look at her as though I had never known her before!), but who looks on the set as though she may be wonderful - although I have seen only a small part of one scene rehearsed..."
Selznick also pointed out that one additional problem that Jean would have to face if she was chosen was to overcome identification with other roles.
 

Paulette was by far the strongest candidate. But there were some issues that needed solving in order for Paulette to be Scarlett. 
Paulette was Scarlett looks-wise, but the problem was if she would be able to carry the part. In order to convince themselves, Selznick and Cukor did numerous tests with her: on February 9, 1938, February 12, February 19 , November 8-9-11, December 8, and final on December 20 and 21, 1938. They included scenes at the bbq, paddock scene, and preparations for the barbecue. As Selznick instructed Cukor in October 1938: "Paulette Goddard has plenty against her in the way of public's attitude, but I think that when it comes time for the final decision she at least has in her favor that she is not stale. F0r this reason, I think George ought to devote particular attention to the dramatic sections of the Goddard test". 
In this aspect Selznick saw an enormous improvement in her work: "I have looked at the new Goddard test - the one she made with Jeffrey Lynn - practically daily since it arrived, to see whether my first impression of the great improvement in her remained; and I must say that each time I see it I am more and more impressed. As much work as possible should be done with her." Paulette was a personal favorite of Selznick, a friend and a neighbor, but there was another issue in need of solving: the public knew that Goddard lived in Charlie Chaplin's house assuming they were married. But Paulette was not able to provide a marriage certificate, even though she insisted she had married Charlie. Selznick, aware of social conventions at that time, hesitated, fearing a possible boycott of the picture.