Personally I like Scott Sonnons Intuflow. I have a few different mobility programs, but I feel like his is the most complete and well thought out.
As far as a quick warmup, I got some advice to do 50 reps of Cuban rotations with 2.5 to 5lb, my shoulders have never felt better. I added internal external rotations in various planes and various hinge movements. To be honest, I almost think I felt better just with the Cuban rotates for 50x no weight, 50x 2.5lbs, and 50x 5lbs.
I started doing something similar with my legs and they feel great.