Polly, i have a Harvard doctorate in Bible and the Early Church.  I was a Theology professor for 12 years and, before that, a Teaching Fellow at Harvard for 2 years.  So I think I know what I'm talking about on the charges your co-worker raised.

Your co-worker is wrong about the King James Version (KJV).  The problem is not what it deletes, but what it includes that is absent from the earliest and best Greek New Testament manuscripts.  The KJV is based on later flawed Greek and Hebrew manuscripts of the Bible that are less reliable than the earlier ones that form the basis of modern translations.  As a result, the KJV contains a host of very minor errors---the wrong word here and there.

But here are its three most serious blunders:
(1) In modern Bible translations, the Gospel of Mark ends with the women discovering the empty tomb. Unlike the other 3 Gospels, Mark contains no resurrection appearances of Jesus.  Many scholars argue that Mark's original ending has been lost.  The greatest error of the KJV is that it adds some resurrection appearance stories in Mark 16:9-20.   These stories are absent from the earliest and best manuscripts of Mark.  The most serious impact of this is the Appalachian sect that picks up rattlesnakes during ecstatic dancing because of the promise in this bogus KJV ending that the true believer will pick up snakes and not be harmed.

(2) The 2nd biggest KJV error is that it includes the story of the woman taken in adultury in its Gospel of John (7:53-8:11).  This story was originally included in the lost Gospel of Hebrews, of which we now have only a few surviving fragments.   Early manuscript tradition shows that it was not an original part of John.  This interpolation is not a serious problem, though, because this lovely tale is a true story from reliable oral tradition.    

(3) The KJV also includes two angel references that are absent from the earliest and best manuscripts. 
Jesus'  healing of an invalid at the Bethesda pool is embellished in the KJV by this verse:

"And they waited for the moving of the waters.  From time to time an angel of the Lord would come down and stir the waters.  The first one into the pool after each such disturbance would be cured of whatever diseased he had (John 5:4)."

The KJV embellishes the story of Jesus' agony in the garden of Gethsemane by adding:  "Then an angel from heaven appeared to him and gave him strength.  In his anguish he prayed more earnestly, and his sweat became like great drops of blood falling down to the ground (Luke 22:43-44)."
The best Greek manuscripts lack both additions.

For a combination of clarity and accuracy you can't do better than "The New Living Translation."  "The New International Version" and "The New Revised Standard Version" are good too.  If you are Catholic, the best version is "The New Jerusalem Bible" (not "The Jerusalem Bible").

Your co-worker is also off-base when he claims,  "Many sections were deleted from the Bible centuries ago that the Catholic church didn't agree with."  Here is the true situation.  The Old Testament canon that Protestants embrace is traceable to the first century and beyond.  The extent of this canon is confirmed by 2 first century Palestinian witnesses, Josephus ("Against Apion" 1:39) and 4 Ezra 14:44-46.  In the 90s AD, the rabbis made it clear that other Jewish writings that might lay claim to biblical status were to be rejected.  Many Jewish apocalyptic writings outside of Scripture had encouraged  the Jews to fight the Romans, with tragic results.  Thousands of Jews were massacred and the Jerusalem Temple was destroyed.

The Catholic Old Testament contains all the Protestant Old Testament books, but adds some Greek books called the Apocrypha that are later than most of our Protestant Old Testament books.  The Protstant Old Testament is restricted to Hebrew books written in Palestine.

From the beginning, our New Testament books were treated as Scripture in various parts of the early church.  By the end of the 2nd century, most of the Christian world acknowledged the authority of the same New Testament books that we recognize.  But not until the 4th century did the church formally delimit a fixed New Testament canon.  Prior to that, there were small pockets of Christians who wanted other books to be treated as equally authoritative: the Didache, 1 Clement, the Coptic Gospel of Thomas, the Apocalypse of Peter, the Shepherd of Hermas, the Gospel of Peter, 1 Clement, and the Epistle of Barnabas.  Of these books, only Didache, 1 Clement, and the Gospel of Thomas have a first century origin.  The others are too late for inclusion as Scripture.  I can't see how anyone who reads these books would want any of them included as Scripture.  But I won't launch into a book by book critique here. 

There were basically 4 criteria for inclusion in the New Testament. (1) apostolic origin: they wanted books with eyewitness connections; (2) relevance to the Catholic church at large; (3) consistency with orthodox Christian teaching; (4) long-standing use as a valued aid to early Christian life and worship.   

Hope this helps,
Don 

Yes, they are all widely available.  People with a Protestant background should read Ecclesiasticus (also called "Ben Sira"), a book in the Catholic Old Testament, but  not the Protestant one.  It's thought world helps fill in the gaps in Jesus' teaching.  For example, it implies that the command, "Love thy neighbor as thyself" is bad advise for a masochist and urges us to develop a healthy self-love or respect before we try to love others.  It also insists that God heals just as much through medical knowledge and methods as He does through faith healing.  Written in 200 AD, it declares that God has imbued herbs with great healing powers.