I note that one version you're considering is NIV. Please no.
There are differences between "liberal" and "conservative" translations, but they are minor. NIV goes further than other conservative translation. For a list of problems, see
Poor and Misleading Translation in the New International Version (NIV)
In general terms, conservative translations see the OT as a Christian book, and where there are questions, tend to make passages easier to refer to Christ. Liberal translations try to translate books as they would have been understood by the author and in his context. The best-known example is Is 7:14. Matthew used it to describe the virgin birth. But if you use "virgin" in the OT, you end up with two virgin births, the first in Isaiah's time. Isaiah surely didn't intend that meaning.
Note Jews tended to see OT events as patterns for current events. Thus John the Baptist was sometimes called Elijah. That doesn't mean that he was literally the same person, of course. For that reason, seeing the birth described in Is 7:14 as referring to Jesus' birth was perfectly legitimate. But if you want to know what the OT mean in its original context, the young woman that Isaiah pointed to surely didn't bear a child while still a virgin. There are other passages in the OT with similar differences.
In the NT, there are minor differences due to theology. They're very rare, but one example is Rom 3:25. I'll talk about that in detail, but there are a few other examples (many others in NIV, of course, but I'm not considering it). This verse contains a term that refers to Jesus' sacrifice. The original is quite general in referring to sacrifice. NRSV and NIV translate "atonement," which is a term that refers generally to Christ's sacrifice, but without expressing a specific concept for how it worked. ESV and HCSB translates "propitiation," which typically refers to a human attempt to appease or conciliate a god. This is consistent with a concept of the atonement called "penal substitution." That's not the only idea of how the atonement worked, and isn't the most common one in the early church.
The lexicon I used (Theological Dictionary of the NT) comments "It is hard to say with any clarity whether Paul in R. 3:25 is thinking of the ἱλαστήριον in particular or a means of expiation in general. Paul does not elaborate his meaning but is content with this summary statement. ... The ἱλάσκομαι contained in ἱλαστήριον naturally does not mean “to propitiate,” as though God were an object. This is excluded by the fact that it is God who has made the ἱλαστήριον what it is. In this whole context God is subject, not object. This is in keeping with Paul’s doctrine of reconciliation (→ I, 255). Only men, or the sins of men, can be object of ἱλάσκομαι (→ 314 ff.)."
