A good place to start with Kaine pre-Scarlet Spider but Post-Clone Saga is Spider-man: The Lost Years although mainly centered around Ben Reilly, Kaine is a very big supporting character and it shows some of the bad choices he's made in the past and what the root of his character truly is. If you are brave enough to go onto the Clone Saga then go ahead! It does pad out Kaine a lot more and delves into how he feels about the Jackal. However this is a story that is not to everyone's taste and really isn't needed unless you're a big Kaine fan like myself and just want to read it because he is in it.
Your next stop should be Grim Hunt as it sets up the basis for Scarlet Spider and begins to show Kaine's change in morals and ethics. This should then be followed by Spider-Island most notably the Amazing Spider-man issues involved in it (as this crossed-over into other Marvel titles). By the time you reach here you should have a good grounding in who Kaine is and what makes him who he is and how he got to where he is now. As soon as you've finished Spider-Island you're ready to move straight on to the current Scarlet Spider series where Kaine is the main character.Kaine's current ongoing Series
If you aren't interested in his back story you can simply skip straight to Scarlet Spider as not a huge amount of his past is brought up and a new reader could grasp the story relatively easily. However if you do want a good grounding in the character those stories I mentioned are the ones I recommend you read.