Any kind of generalized strength training will help. If your teacher says otherwise you should find a new school to train at.
You can lift weights without trying to be a bodybuilder. Squats and deadlift will give you a good foundation of strength in your legs. Deadlifts will also help strengthen your lower back so that as you age, you are less prone to lower back injuries than the average person. Bench press and overhead press will strengthen your chest, anterior deltoids and triceps. Pullups will work your lats and biceps, and since you're an ectomorph like me, pullups should be attainable for you Biceps curls for the biceps. Calf raises for the calves. Shoulder flies for the medial and anterior delts. That's pretty much your whole body unless you want to throw in shrugs and ab work.
If you do cardio and weightlifting on the same day, lift weights first. Lifting weights when you're fatigued from cardio could result in injury.
Ideally I wouldn't lift weights on the days you train Hapkido.
When when you start lifting weights, you'll probably be sore, so take it easy. Going to hapkido class with sore muscles might not be a very fun experience. The more your body gets used to lifting, however, the less soreness you will get.
The first time I do squats, for example, after taking time off, my legs are sore and walking hurts for 4-5 days. But once I'm in the routine of things, my legs are like just a little bit sore the day after and that's it.
Just go slowly at first. It can be easy to over do the weightlifting when you're starting.
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