> And core strength helps prevent back pain
Sounds like a sales pitch for deadlifts.
Deadlifts are probably the most trainable movement for building strength in the most muscles, and muscles (upper back) that are weak if you sit at a desk.
I think the key to getting strong is barbell exercises, because they can be precisely and incrementally loaded. (So you linearly progress.)
> And core strength helps prevent back pain.
Deadlifts, squats, and presses are all extremely good at developing "core" strength. Ab-specific exercises are not (they cannot be effectively loaded, and the loads are much smaller, and the spinal flexion/extension involved often aggravate existing back injury).
> chair that helps you sit up straight, and provides lumbar support.
If the chair is helping you, then you are not using your muscles and will continue to atrophy away. Lumbar support in general is not a good thing.
You need the upper body strength to avoid supporting yourself on your wrists. They should just "float". Having good forearm support helps, but it's not enough if you're weak.
And core strength helps prevent back pain. Along with a chair that helps you sit up straight, and provides lumbar support.
Wrist curls and reverse wrist curls have also helped me a lot, for both wrists and elbows. I also use self-practice wrist locks for strengthening and stretching. Or with a rubber torsion rod.