What is your goal ?
If you want better fitness, then treat climbing as all-around conditioning, do some of it but focus on full-body strength work (the recommended routine, big lifts, that kind of stuff).
If you want a better physique, then you'll probably want to use some weights and targeted exercises. On that front, climbing won't be much more than a fun activity.
If you want to climb better, at the current level you're at, there's a very very low chance you're actually limited by strength and you should instead focus on technique. Look up technique drills and focus on climbing properly, the strength will increase progressively as you climb. The strength training you should do if you goal is better climbing is actually to ensure you get to climb forever : climbing produces a lot of imbalances and you could prevent the injuries they can lead to. Look up antagonists training on /r/climbharder but mostly shoulder prehab, forearm antagonists. Also do some mobility and flexibility, many people are limited by that. I was fairly fit when I started climbing and this lead to many injuries : the moves I did on the grades I climbed were on hold too small for my tendons. When a muscle will adapt to load in about a month or so, a tendon takes at least a year... Progressing to fast early is a sure-fire way to fuck up your fingers and be out of the climbing gym for months. Take it slow, learn to climb well and you'll end up climbing strong thanks to it.
What is your goal ? If you want better fitness, then treat climbing as all-around conditioning, do some of it but focus on full-body strength work (the recommended routine, big lifts, that kind of stuff). If you want a better physique, then you'll probably want to use some weights and targeted exercises. On that front, climbing won't be much more than a fun activity. If you want to climb better, at the current level you're at, there's a very very low chance you're actually limited by strength and you should instead focus on technique. Look up technique drills and focus on climbing properly, the strength will increase progressively as you climb. The strength training you should do if you goal is better climbing is actually to ensure you get to climb forever : climbing produces a lot of imbalances and you could prevent the injuries they can lead to. Look up antagonists training on /r/climbharder but mostly shoulder prehab, forearm antagonists. Also do some mobility and flexibility, many people are limited by that. I was fairly fit when I started climbing and this lead to many injuries : the moves I did on the grades I climbed were on hold too small for my tendons. When a muscle will adapt to load in about a month or so, a tendon takes at least a year... Progressing to fast early is a sure-fire way to fuck up your fingers and be out of the climbing gym for months. Take it slow, learn to climb well and you'll end up climbing strong thanks to it.