Are Christians supposed to be Christ-centered or Trinity-centered?

Fred Sanders answers the question well:

We need to see, as clearly as possible, that the gospel of the Trinity is not an alternative gospel to the experience of personal salvation through Christ. There are not two different messages here but a single proclamation of good news that is simultaneously Christ-centered and Trinity-centered. There is never any need to play the doctrine of the Trinity off against salvation in Christ, because they are centered on the same reality. The more Trinity-centered we become, the more Christ-centered we become, and vice versa.

The main reason that a Christ-centered message can never be in real tension with a Trinity-centered message is that the two messages are concentric. When you declare that Jesus Christ is the center of your message, you are committing yourself to proclaim Him and whatever is central to His own concerns. But Jesus Himself is always centered on the work of the Father and the Spirit, so successfully focusing on Christ logically entails including the entire Trinity in that same focus. It is incoherent to hold to Jesus without simultaneously holding to the Father and the Spirit. (Taken from The Deep Things of God, p. 167-168)

For a short introduction piece on the Trinity and its essential importance to everything (not an understatement), check this out. For some good books on the doctrine of the Trinity I recommend the following (in order from shortest to longest):

• Delighting in the Trinity: An Introduction to the Christian Faith by Michael Reeves (135 pages)
• Father, Son, and Holy Spirit: Relationships, Roles, & Relevance by Bruce Ware (176 pages).
• The Deep Things of God: How the Trinity Changes Everything by Fred Sanders (quoted above; 256 pages).