Was Hitler effective as a strategist during September 1939-1941?Essentially, was he making strong choices during his decision to attack Poland through Barbarossa?
Actually, Operation Barbarossa was the plan to attack the Soviet Union; not Poland. The invasion of Poland was Operation Fall Weiss ("Case White") There is certainly strong argument that Hitler overplayed his hand by attacking Poland; but interestingly he met with a number of successes after that, including his successful invasion of France and Denmark. His greatest mistake seems to have been his invasion of the Soviet Union. Had he kept his word from the Soviet-Nazi Pact in which the two agreed to divide Poland, it is entirely possible that a negotiated settlement of the war might have been reached and Germany would have made sizeable gains. His fatal flaw was that latter invasion. He was warned by his advisors that attacking Russia had brought down Napoleon. Hitler insisted he knew Napoleon's mistakes, and would not repeat them. His troops were brought down by the same Russian winter as was Napoleon.
So, I think he was a strong leader up to the point of the Soviet Invasion. In fact, the historian R.G.L. Waite in The Psychopathic God argues that if Hitler had died in 1939; he would have gone down as the greatest German leader in history.
I would have to say that Hitler was not an effective strategist because attacking Poland and causing the war to start was not a smart move. If you assume the war was inevitable, then he was much more effective.
Strategically speaking, Germany needed to stay out of a big war that was going to last a long time. Hitler miscalculated and got Germany into just such a war. First, Hitler did not believe that the Allies would actually go to war over Poland. He was wrong about that, obviously. That was a major strategic blunder. Second, Hitler believed that the British would make peace with him once he had control of Western Europe. He was, once again, wrong.
Because of these mistakes, Hitler ended up (pre-Barbarossa) in a stalemated war in which he was unable to touch his major enemy. This was not a great position to be in. Of course, things weren't so bad at this point. It was only with Barbarossa and, later, his declaration of war on the US, that Hitler really made his biggest mistakes.
Yes, there is a sense in which Hitler's arrogance and his belief that he could ride roughshod over the sovereignty of other European states resulted in a severe miscalculation that made Germany enter a war that it did not want. However, just to look at the alternative perspective for one moment, it is easy to see why Hitler felt he could invade Poland without any recriminations. After all, he had done the same thing with Czechoslovakia without any problems whatsoever, and Neville Chamberlain and the other European powers seemed rather more preoccupied with protecting themselves rather than attacking him. Thus, although we can look back and say that strategically his invasion of Poland was not a wise move thanks to the war that it triggered, we could also argue that it was by no means clear that his invasion would lead to war.
Everyone will have his or her own personal opinion about matters like these, but when considering such matters I always like to get the opinions of experts. As it happens, I just found a site that may be of special interest to you. It offers a transcript of discussions by historians about the very question(s) you have raised. Here's the link:
Reading these kinds of discussions is fascinating. I love the give-and-take of any real exchange of ideas, and it looks as if this exchange may be especially worth your time.