If I had to pick one area it would be shoulder stability and posture stuff:
Rotator cuff-- band or cable internal/external rotation, lying dumbell raises. Scapular pull ups and push ups. Sots press with a 10 or 25 lb plate super glad I found this one. These go along well with broomstick shoulder stretches and completely fixed my climber postural issues.
And my other favorites, in no particular order: deadlift, bench press, deep one legged squats, hanging leg raise, hip mobility/weighted leg raise. I don't go crazy with pushing the weight and focus more on form and quality sets. Running. I actually enjoy working out for its own sake hence the long list. Climbing is a good way to center an entire physical practice.
I am not on the weighted pull up bandwagon, at least for now, have seen it stiffen climbers' movement and lead to an upper body centric movement style, like they are constantly climbing on terrible hand/footholds even on easier terrain. I also don't like pullups and it looks super not fun to me. Though I did do a lot of lat pulldowns for a few years and now seem to maintain whatever level of pulling/lockoff strength I need through "just climbing."