In May of 1940 Hitler had defeated France and the British Expeditiary Forces that were fighting alongside the French. He had all options open. He decided not to invade England between June - August while the weather would have still permitted it. He decided not to kick the British out of Northern Africa which would have allowed him to attack Russia from two fronts and would have given him easier access to the oilfields in the Caucasus. Instead he geared up for an entire year and committed everything he had to Operation Barbarossa. It failed in 1941 and this had little to do with the British or Americans. It was an all-out war in 1941 between a German Wehrmacht that was at the pinnacle of its military might and the Red Army and the Wehrmacht was unable to defeat the Red Army.
Again, you are not taking into account the stress Britain put on Germany's industrial military capability. Britain is an island and thus the Germans could never invade it, and the Royal Air Force starting in 1940 bombed Germany's heavy industry on the Rhine almost daily. This combined with the fact that the Wehrmacht was always bailing out the incompetent Italians in northern Africa, plus the heavy civil resistence in occupied Eastern Europe, put a great deal of strain on Germany and significantly aided the Soviets. This, combined with the fact that the Russians had 3 times more heavy industry, 2 times the population, 4 times the oil and knew the territory much better because they were fightring at home, made it almost impossible for Germany to win. And BTW, the Wehrmacht got to Moscow's suburbs and almost took it.
As for what you said about Hitler's options, he would have to take several nations before he could hit Russia from the south, and it's doubtful whether that would be somehow superior to hitting Germany from Eastern Europe. Germany's Waterloo was Stalingrad, and that's because Hitler insisted on taking the city instead of just wiping it from the face of the Earth. If I were Paulus, what I would have done would be to move my troops in two split groups, one to the south and the other to the north, then enveloping the city from all sides, barricating the city and stopping anyone from fleeing, and then just bomb the city to rubbles from the air and with long-distance artillary. That would have been the smart thing to do. Eventually, the few survivors would surrender and the battle would have been won with the Red Army troops locked inside the city unable to flee or fight back. But Hitler was a proud man who wanted to simply conquer the city in a direct assault, for no other reason than the city was named after his arch-nemesis, and he wanted to humiliate Stalin. Hitler's arrogance and obsession with man-to-man combat - to prove the superiority of German warriors - cost him the war.

SUCKMYMUSCLE