There isn't a "First Rainbow Six" book... there is
A Rainbow Six book u plonker.

You do realise that 9/11 was Clancy's fault don't you... Debt of Honor was all about a Japanese pilot crashing a 747 into the US capitol building at the end of the book and the next book, Executive Orders, was about Jack Ryan taking over as president and punishing the ones who did it. Come to think of it if it was Terrorists ideas at the end of Debt then Executive Orders was about George W Bush's war against Iraq (only it was Iran in the book).
To really read Clancy you have to start at the beginning of the Jack Ryan series... those are the good ones. The Netforce ones are OK but steer clear of the Power Plays series... Utter boredom imho (although I still have read them as I just hoped they would be OK). Netforce Explorers are kiddies books and I have yet to read any game related (other than Rainbow Six) books of his.
The one book I do remember enjoying was Red Storm Rising... a one off early novel about a US vs Russia war in the 90's before all the heavy tech changed the US war machine.