Congratulations on your purchase!
The Bible is absolutely fine. The NRSV was translated with Catholic and Protestant participation; and also included an Eastern Orthodox and a Jewish translator. It is well established as a standard translation. The Catechism of the Catholic Church quotes from it extensively. It used for liturgy in Canada. It is a standard text in many Catholic colleges and seminaries.
Your volume probably includes a statement of the books that are in various canons (Jewish, Protestant, Catholic, Eastern Orthodox). If not, you can find a complete listing
here. You can print out the table and paste it in your Bible. The extra books from the Eastern Orthodox canon are two extra books of Edras (and these are in an appendix to the Latin Vulgate), Prayer of Manasseh, Psalm 151, 3 Maccabees, and 4 Maccabees. In most NRSV editions, these are all together, and you can easily mark them in your Bible.
The Catholic books of the NRSV do have the imprimatur – in fact two: both of the US and Canadian Bishops’ Conferences. If you need confirmation, you can find it at the USCCB web site
here.
Some people like the NRSV and some people do not, but reading it will not “harm” you (any more than reading the Deuterocanonicals will harm Protestants). It will expose you to the common books held sacred by Jews, Protestants, Catholics, and Eastern Orthodox. Keep in mind which canon each book belongs to.
And don’t forget to pray for the unification of the Western and Eastern churches.