I think reading the Bible is a good language learning technique if you already read the Bible in your own language. I say that because what you already know about the Bible will help you to understand it in English.
Any recent English translation could be good if you want to learn current English. There are also more traditional translations out there like the King James Bible. The language is poetic, but it is not current.
I should also add that, as you might expect, different Christian denominations prefer different translations. For example, my family is Catholic, and I think they read the New American Bible. I remember the language being relatively accessible.