I agree with Elite, but it kinda depends on which story ark you want to follow (they merge in many books)
John Clark aka Kelly = bad A navy seal now CIA and later head of team rainbow
or
Jack Ryan= CIA analysis and stuff (i would tell you but i consider it a plot spoiler)
speaking strictly chronologically the plot follows Jack Ryan the most
according to Wikipedia
Jack Ryan/John Clark Universe
* Without Remorse (1993) (John Clark, Jack's father Emmett Ryan)
* Patriot Games (1987)
* Red Rabbit (2002)
* The Hunt for Red October (1984)
* The Cardinal of the Kremlin (1988)
* Clear and Present Danger (1989)
* The Sum of All Fears (1991)
* Debt of Honor (1994)
* Executive Orders (1996)
* Rainbow Six (1998) (John Clark, Jack Ryan by reference)
* The Bear and the Dragon (2000)
* The Teeth of the Tiger (2003) (Jack Ryan Jr.)
http://en.wikipedia.org/wiki/Ryanverse
Without remorse is quite violent (well more graphic) however don't let it put you off, most of the books aren't (considering your playing CA it shouldn't put you off)
either way both Red October and without remorse are good starting points.
I read Hunt first.