Done a bit of climbing myself but Im by no means an expert. Firstly its much more important to have good technique, although strength obviously helps in certain situations. The instructor guy I used to see was a fairly small guy, decent forearms of course but great endurance ability.
For excercises the obvious ones are forearm / grip work, pull-downs / pull-ups. You need strength but probably more important is total body endurance so Id say static holds might help. Its not all upper body as well, any one limb may end up having to take most of your weight at a given time so dont neglect your legs.
As you progress you’ll find yourself in crazy positions like hanging on to tiny grips with two fingertips of each hand and having to swing a leg up to get your foot to the next point thats like 2 meters above and to your right!! So you need flexibilty as well.
First time I went climbing I thought “No problem, Im in shape, I do my pull ups” and thought Id muscle my way up. The training walls were easy and fun but the harder walls were well… harder! Its more aerobic than it looks too so cardio and GPP will help.
All things considered the best way to get better is by actually doing it!! And a good teacher is invaluable.
Hope this helps, its a good sport/hobby to be into.
Hell Im in the mood to go climb now…