If I want to buy a copy of the Bible, which version does one buy that would be the official Roman Catholic version?
It seems the Kings James version is the most popular, is that the one?
Will this contain both the New and Old Testament?
The Official Bible is the Vulgate, translated into Latin from (mainly) Greek by St. Jerome in the 4th Century after the canon was finally established.
If you're looking for an English translation, any Bible with an imprimatur should be good. I wrote another answer here a while ago about whether Catholics can read the NIV that might be of use to you. The point is, Catholics should look to the Church for official interpretation no matter what the translation is.
There is a list of several approved English translations published by the USCCB. The Vatican has a copy of the New American Bible on it's website. These translations include the New Testament and the Roman Catholic Old Testament Canon.
The King James Version is a popular translation for English-speaking Protestant Christians. It contains the New Testament and the Protestant Old Testament Cannon. There is a subset of conservative English-speaking Christians that consider it to be the only authorized version of the Bible but for most English-speaking Christians it is only one of many popular translations.