You’ve asked a perennial question of biblical theology, one that, as you also point out, began with the Apostles themselves. How do we understand Paul?
That said, I don’t know how to answer the more specific question of how to understand Paul, without exploring the broader question first, of how to approach the Bible in general. I think as an Evangelical Protestant myself, it is necessary to have a good understanding of what the doctrine of Sola Scriptura does and does not entail. When we understand that Sola Scriptura does not mean, nor according to the first wave of Reformers ever did mean, “scripture only” then we can proceed to develop a good method for understanding any part of the Scriptures, because we will approach the Bible with the right method and, hopefully, in the right attitude.
Thus, to understand Paul, I would suggest that first we try and get a grip on the larger story of the whole Bible. Then, after that we would want to move toward more specific contexts, like the New Testament, then all of the Pauline letters, then the specific letter of Paul we are examining, then the part of the letter and the immediate context surrounding that part. This is a basic heremeneutical principle, moving from the larger to the smaller, the broader to the more specific, and one that can be easily done. You read quickly through the larger portions and then engage more slowly with the smaller ones. Since you probably already know the larger story of the whole Bible, and the NT, you probably could already begin with Paul in general, or maybe even with a particular letter, like 1 Corinthians. If you start with the letter itself, read the whole thing five or six times fast, then read the chapter your passage is in a few times, then hone in on the passage itself.
Second, background context can also provide us with greater insight into any passage of scripture. Background knowledge could be categorized into two domains: 1) historical and cultural background, and 2) literary and genre background. The first category will tell us much about the everyday world that Paul was living in, which will help us understand particular references to people, places, things, and concepts of the day. The second category will help us understand the structure, shape, and language of the Biblical texts themselves, and how the authors intended their writing. So, first principle would be to understand broader contexts first, then move toward the more specific, while the second principle would be to understand background data that will help clarify passages of interest.
Third, we would, if possible, want to know the original languages. If this isn’t something we really can entertain, or at least not in the moment, then we have to rely on experts who have the required linguistic training and their exegetical work. There is nothing wrong with relying on experts, but it just means that what we will have to do is try and read a balance of the experts who have written commentaries on said passages and then weigh and evaluate their conclusions. So, at this point we are moving from just reading the Bible, to reading experts who have read and studied the Bible in its original languages. A good way to know that you are accessing the right kinds of materials is by getting a resource like these here that guide you to the best commentaries on OT and NT books:
Using these surveys can help you access the best commentaries on whatever book of the Bible you are interested in. Also, most commentaries, the good ones at least, will already have detailed discussions of the background data you need that I mentioned in step two.
At this point you are beginning to exhaust those sources of knowledge that we might file under Scripture directly. Once you start reading through the material yourself, you now have to use reason to guide you. As I already pointed out, you will have to weigh and evaluate competing conclusions by the biblical commentators, not to mention your own rational engagement with the text itself. Also, your experience of the world you live in will be a part of your understanding of Scripture, so your interpretation will have some degree of subjectivity to it. This is not to say that there is no objective truth that Scripture imparts to us, but that there is always some subjectivity to our interpretations, and that is okay so long as the Holy Spirit is guiding the whole process. After all, God wants us to connect the objective truth of Scripture to personal and concrete realities in our own life, and in the life of the Church today. This “illumination” is part of the Spirit’s role in bringing Truth that is relevant to our own context.
Finally, however, we should also be aware of the traditions of the church. Tradition is also part of the doctrine of Sola Scriptura, regardless of what you may have heard from those who don’t fully grasp the concept, or who might be exercising some kind of polemical project against the Reformation view of Revelation. Thus, we do look to church history and the history of interpretation as a guide and a safety-net to prevent us from straying too far from that objective truth of scripture that truly is binding on all believers throughout space, time and culture. We do this, even if we also recognize that tradition can, in principle, be broken with, or revised, if, after much thought, reflection, and wrestling with the text itself, a given traditional interpretation no longer seems to be correct. Scripture ultimately forms our traditions, even if traditions and traditional interpretations, especially ones that have stood the test of time, help us interpret Scripture.
In sum, start with the text of Scripture first. Then read things about the text of Scripture (historical background data, literary and genre information), then look at the best commentaries by people who have mastered exegetical practices, then engage with the traditional interpretations of the Church (both Catholic and Protestant), especially those written by men and women known to be definitive voices (e.g. Augustine, Aquinas, Luther, Calvin, Wesley, etc), then use your own powers of reason and carefully consider your own experiences of God in Christ and the experiences of your local church community. Then discuss your findings with your local church community and see where there is a agreement or divergence with your brothers and sisters in Christ.
Of course, beyond this process itself there are already scholars who have done most of this work for us, as @Jimmy_Sellers alluded to with N.T Wright, who is one of the top Pauline scholars in the world today, albeit not the only one, which is also important to note.
Finally, and I leave the most important point for last, approach this whole process in the Spirit of God. Approach God’s Word in humility and in prayer, and I believe God will honor you with the knowledge of what He allowed His servant Paul to convey to His church.
I hope this helps.