Presumptuous. That would be a middle school coach pontificating about the 'proper' shooting warmup.
What I can offer is some perspective and caveats. I hate seeing young players walk onto the floor and start jacking up threes. It reminds of the story of the guy getting his AM newspaper on his front walk and sees a snail. He picks it up and flings it across his yard. Two years later, he sees the snail again, picks it up and the snail yells, "What was that about?"
1. Your warmup begins with your mental preparation. I believe that having a 'mental warmup' before games makes sense because stress degrades performance. Of the sports psychology books I've read, the two I favor are Jason Selk's 10-Minute Toughness and the Weisinger and Pawliw-Fry work Performing Under Pressure. Selk provides a very specific routine tailored to each individual. I've attended lectures about mental preparation by Dr. Tom Hanson, who worked with an unnamed future Hall of Fame shortstop. Amy Cuddy's TED talk discusses the role of body position and hormonal responses to stress. It's worth the watch.
2. Time is a premium. First, in our area, for the games that matter most, e.g. sectional championships, the amount of formal warmup (because of multiple game scheduling) tends to be very brief, e.g. 10-15 minutes, tops. I've seen it less when games run over. So, if you expect to get thirty minutes, good luck. It's not happening. So you might think about developing a "rapid warmup" if you expect to be playing in those contests. That's why I consider mental preparation SOP.
For more generic shooting (after your individual/team stretching), professionals have their routines. They reinforce their form, touch, and see the ball go through the strings.
3. Purify your form. Form begets function. I believe in Fred Hoiberg's approach.
When I attended a UCONN women's practice, each player also followed this routine.
4. Process begins with the small things. J.J. Redick starts by making 20-25 shots from each block. He then moves into working into his game shot routine.
5. The magic is in the work...that works for you. I remember Elden Campbell saying that he would start along one baseline and make five consecutively, then wing, foul line, wing, and opposite baseline.
Great players have idiosyncratic warmups. Ray Allen used to take several hundred shots. You don't have the time or the rebounder to do that.
Kevin Durant works on some of his favorite shots.
As I reminded one of our players last night, "Repetitions make reputations."
