based on articles
if Jack Kirby had suggested the idea to Stan L ee than Kirby is the creator of spiderman though his custome was rejected. He may not be the creator of the custome but he came up with the idea and first design.  It seems weird that Ditko would admit kirby had involvement and stan lee denies. Some evidence might be missing esp. due to the fact kirby suggested and created it when not working for Marvel. Stan lee seems to have stolen the idea and published it but that doesn't mean  he created spiderman. In the name Spider-man  or spiderman  there is no difference actually. Spiderman resembles kirbys creation. His family members are not proof nor do they deserve money.  
 
   

Lee and Ditko obviously.  Even if Kirby suggested the idea, he still doesn't deserve credit.   An idea is one thing, a finished product is another completely.  Lee and Ditko did the work and they deserve the credit.....well probably Ditko more than Lee XD.  It takes a lot more evidence to claim the creator credit than a crappy costume that looks like Captain America.

Only thing I've ever heard of regarding Kirbys involvment is that he drew the cover to Amazing Fantasy # 15.
Even if he put forward the name there's a lot more to creating a character than that. Stans characters have a certain style to them that Spideys has. Kirbys ideas were always a bit more far out. The New Gods for instance. Even a non comic fan can see the huge thematic differences in their creations.

Lee and Ditko but Jack Kirby did make contributions to the character and he drew the cover for his first appearance

According to the book about Ditko, Strange and Stranger: The World of Steve Ditko, Kirby came up with the idea that a young boy (living his his angry Thunderbolt Ross type military father, and living next to a scientist) gets a magic ring that turns the young boy into the adult Spiderman.  Kirby did about 5 pages of his idea and submitted them.  Somewhere exists his Spiderman pages, proof of how much of his idea was used.  According to Ditko Kirby's idea was too close to his previous idea for the Fly, so Stan wrote a synopsis that he and Ditko submitted their idea about ayoung teenager who gains powers, the death of his uncle Ben, getting more problems once he became Spider-Man, and all that.  So, from what the book says, Lee came up with the main idea of Spider-Man that everyone loves and Ditko came up with the costume, as well as several other story elements that make Spider-Man who he is like Spider-Man's poses.  As for Dikto creating the costume, I read some place that Ditko was angry at Lee because Lee thought because the concept was his idea that he created Spider-man even though Ditko brought him to life and was in charge of the comic since issue 10.  He says he came up with the costume and all the visuals and most of the ideas, like keeping the character down to Earth.  So He sort of claims, I think, that the costume was his idea.
Ditko also says this was his cover: 
 

a great comic mystery that will never be solved