I have read of a theory or three that J.D. Tippit was involved in the "conspiracy."  Not as the shooter (that I've read), but that he was assigned to kill the "assassin" Oswald to keep him quiet.

If you want to get more of a handle on Oswald, read Norman Mailer's OSWALD'S TALE.  Mailer based much of his book on the no-longer-secret KGB files on Oswald's stay in the Soviet Union.  The KGB found, pretty much as US intelligence did, that he was an odd, slightly "off" malcontent.  Even if you don't accept that Oswald was the lone nut assassin, it's still pretty clear that he was a loner.  And a nut.

If you want to know what God thinks of money, just look at the people he gave it to.                                                                                     Dorothy Parker