Best gym exercises for basketball?

Basketball has been my biggest motivator for exercise for a while now, and despite my size I have the fundamental skill to play recreationally, but I'm looking for advice on a few things:

1) Endurance - right now, I run 1x a week (~40 mins, and I alternate run/walking doing couch to 5k-type-intervals), play basketball 1x a week (~60 mins), and play another sport usually 1x a week (either another basketball session or tennis or something similar for 45 mins). I also walk about 20-30 minutes minimum about 4-5 days a week and do a low-impact (the treadmill hurts my knees, but basketball doesn't) cardio exercise for 30 minutes once or twice a week at the gym. Trying to find a way to stay energetic after running the court a couple times. I want to add consistent (something other than doing 100-150 crunches 2-3x a week as I have been) strength training, 2-3x per week, that will help with this.

2) Core strength: I feel like I'm unbalanced when I'm running full speed, so I find myself holding back sometimes - my arms and legs feel 'floppy' and others have suggested I work on my core to help with this - thoughts, beyond more crunches?

3) Flexibility: Probably just being so large, but I struggle sometimes with the fast side-to-side movement. I've heard to work on hips, but I'm looking for specific exercises.

The advice is appreciated! Obviously, I should focus on losing more weight through both diet and exercise (I know that every pound makes it easier to move). Still, I'm a really competitive guy when I play with my friends or brother and I feel like my performance has only narrowly improved despite being in better shape (I've seen huge gains in my distance/endurance for running, as an example).