2) If we are going to "believe in" the Bible, how do we know which version to choose to believe in?[snip]
3) Wouldn't such a choice have to have some reasons for it?

From a Christian perspective, I'd say we do not "believe in" the Bible but accept it as God's word or teaching but maybe you would consider that hair splitting.

A Christian would choose a Christian bible. Within this I believe there are a couple of differences in the books contained in the Roman Catholic, Eastern Orthodox and Protestant cannons so the denomination might make a difference.

Apart from that, I think reasons of making a choice would include:

Having a common Bible for a group, eg. a church.

The language used in the translation. Personally I choose the New International Version as I find it easier than say the older English in the King James version without (I suppose) becoming too "simplified" in the use of the English language. Another person may prefer the (I'm told) more poetic style of the KJV, etc.