Previous posts include:
1a. Born at a Time and Place 1; 1b. Born at a Time and Place 2
2a. A Change in Life Direction; 2b A Change in Life Direction 2; 2c A Change in Life Direction 3
3a. The Unknown Years 1; 3b. The Unknown Years 2; 3c. The Unknown Years 3
The previous posts for the current chapter are Life Beyond Death 1; Life Beyond Death 2; and Life Beyond Death 3.
[Some scholars have also suggested that Paul's thought underwent development between 1 and 2 Corinthians on the question of when resurrection takes place.  Whereas in 1 Corinthians 15, Paul clearly thinks of us receiving our resurrection body at the time of Christ's return, 2 Corinthians 5 says that if the "earthly tent we live in is destroyed," if we die, then we have "an eternal house in heaven," our resurrection body. It would be easy to read this statement to indicate that we go to heaven when we die and get a spiritual body immediately at death. We want to please Christ whether here in the body or in heaven when we die (2 Cor. 5:9). And one might argue accordingly that our appearence before the judgment seat of Christ in the next verse (2 Cor. 5:10) is what happens immediately at death.]
Although this is a possible interpretation of Paul, most scholars have not opted for it. It is possible to interpret Philippians and Romans with this slightly different understanding of the timing of resurrection (i.e., that it takes place at death). But it does not seem the most natural reading of, say, Philippians 3:11. These two letters were written either about the same time or a little later than 2 Corinthians. On the other hand, 2 Timothy 2:18 warns of those who say the resurrection has already happened. Could it be a warning against the kind of teaching we are talking about?
Looking at these sorts of questions in detail can be a little startling. For example, popular thinking usually stops with "you die and then either go to heaven or hell." Some so equate the idea of the immortality of the soul with bedrock Christian faith that they might even react with anger to hear what resurrection was really about in the Bible.  Meanwhile, the notion that we will reunite with our bodies is not attractive to many today, just as it wasn't to some in Paul's own day. The idea of resurrection was foolishness to some Greeks--why would I want this "prison house of the soul" back again. And the idea that the resurrection is an event still on the horizon can disrupt some comfortable sense of dying and then immediately going to our "final resting place."
Scholarly debates over the meaning of various passages can also be confusing, even disturbing. You mean those who know the most about these issues find room in the evidence for disagreement? Did Paul's thought develop in some ways over time? It implies a rethinking of the Bible as a single, static book whose "chapters" all say the same thing. It pushes us to read the Bible more as a library of books than a single one. Now we have to get a sense of the biblical trajectory rather than assume Genesis teaches exactly the same things as Revelation.
For example, on this particular issue, the Old Testament as a whole has little to say about the afterlife at all (e.g., Ps. 30:9; Eccl. 9:4-6). The only passage in the Old Testament that everyone agrees points to a meaningful, personal, conscious life after death is Daniel 12:2-3. The New Testament thus seems to take us further along on a trajectory of revelation than the Old Testament on this issue.
Many of the beliefs we have on issues like the afterlife seem obvious to us in Scripture. But the reason is not always because it really is clear but rather because of a certain common sense we have inherited from the Christian traditions of which we are a part. Some of these traditions are rather recent, like the idiosyncratic beliefs of churches that only came into existence in the last century or so. By contrast, the best "common sense" readings are those that the Christian Tradition (big T) arrived at by hashing out these sorts of ambiguities throughout the ages. Presumably God's Holy Spirit has had something to do with such common Christian faith, such Spiritual common sense.
On the afterlife, Christians have affirmed since the beginning, "I believe in... the resurrection of the dead and the life everlasting" (the Apostle's Creed). We have affirmed this resurrection as something that is yet to come (except for Christ, the first fruits of the dead; 1 Cor. 15:20) and that will involve continuity with our human bodies as possible, although transformed into something that cannot decay. Christians throughout the centuries have affirmed that our souls will continue to exist and be conscious in between our deaths and our resurrections.
Christian tradition throughout the centuries has generally looked to a similarly transformed creation, a new earth. Paul is not entirely clear where he thinks we will spend eternity, but he does clearly speak of the redemption of the creation along with the redemption of our bodies (Rom. 8:19-23). It is perhaps more likely than not that he saw us living out eternity on a new earth with new bodies not made of the old flesh and blood (1 Cor. 15:50). Many Christians think of us spending eternity in heaven, and there are some New Testament passages that can be read this way (e.g., John 14:3; Heb. 12:26-27; 1 Pet. 1:4; 2 Pet. 3:10). But perhaps throughout the centuries, more Christians have believed we would spend eternity on a new earth (e.g., Rev. 21:2). God will clarify all these ambiguities when He ushers in His kingdom.
 Although he possibly makes things a little more tidy than they really were, an excellent introduction to this entire topic is N. T. Wright's, Surprised by Hope: Rethinking Heaven, the Resurrection, and the Mission of the Church (San Francisco: HarperOne, 2008).