CJ Mahaney has some helpful posts on the believer’s adoption. Here’s a great quote from J.I. Packer he includes:
That justification—by which we mean God’s forgiveness of the past together with his acceptance for the future—is the primary and fundamental blessing of the gospel is not in question. Justification is the primary blessing, because it meets our primary spiritual need. We all stand by nature under God’s judgment; his law condemns us; guilt gnaws at us, making us restless, miserable, and in our lucid moments afraid; we have no peace in ourselves because we have no peace with our Maker. So we need the forgiveness of our sins, and assurance of a restored relationship with God, more than we need anything else in the world; and this the gospel offers us before it offers us anything else…
But contrast this, now, with adoption. Adoption is a family idea, conceived in terms of love, and viewing God as father. In adoption, God takes us into his family and fellowship—he establishes us as his children and heirs. Closeness, affection and generosity are at the heart of the relationship. To be right with the God the judge is a great thing, but to be loved and cared for by God the Father is greater.
Knowing God (IVP, 1993), pp. 206–207.