One possible approach you might take is to look into elements that you particularly liked from the Abrams movies. Keeping in mind that the novels show a possible version of the characters and situations, of course.
If you are interested in understanding a version of the history of the ship itself, Diane Carey's book The Final Frontier gives a story of what her maiden voyage was like, as she was originally in service long before Jim Kirk even entered Starfleet. And for a possible version of the TOS character's first adventure assembled together on the Enterprise there's Vonda McCintyre's Enterprise The First Voyage.
If you're interested in Spock and Vulcans, perhaps Spock's World and Vulcan Academy Murders.
The writers of the Abrams movies took inspiration from some of the novels, myself and someone else already mentioned Spock's World; and Best Destiny shows Kirk as someone speeding for a life of crime, with his father figure (his actual dad, George Kirk, briefly seen in the first Abrams movie) guiding him to a life were he realizes he could fulfill his potential better. This might make the experience of the Abrams movie more satisfying as you come back to them and watch Christopher Pike become a the father figure that Kirk needed to help guide him.
Judith and Garfield Reeve-Steven's novel, Prime Directive, was also cited as inspiration for the writing of the Abrams movies, and I thought for a time, based on the teaser synopsis and trailers for ST Into Darkness that the new movie was going to echo Prime Directives storyline. At the end of the day, Prime Directive demonstrates how serious an issue the Prime Directive can be, and what sort of trouble a starship captain can bring down on themselves if they play too fast and loose with it.
I get the impression ST Into Darkness took strong inspiration from elements of the novel Dreadnaught!, particularly note how the Vengence is identified as a Dreadnaught-class starship. You could look at the book as an explanation for how the Dreadnaught-class starship development program played out the first time for Starfleet and the Federation.
There's a novel called Kobayashi Maru, which you could take as a version of how Kirk beat the test in the original version of ST.
If you're interested in Khan, you can always give Greg Cox's Eugenics Wars books a try, for a possible explanation of where the character is coming from.
There are a number of comics that tell different versions of the stories as well.
And of course, if you can give details on what aspects of the new movies you liked in particular, there are plenty of posters on here who can guide you to books that will at least offer a version of how those details and elements are fleshed out in the original version of TOS's unfolding narrative.
Hope that helps.