The problem with the "take Caucuses and oil" strategy is that Stalin was expecting them to do exactly that. The cream of the Red Army was in the south. Hitler, in fact, ordered that the main thrust be in the south, but OKH Chief of Staff Franz Halder went and reoriented the operation against Moscow, then lied and said the main thrust would be in the Ukraine. The Reds were unprepared for Germans in the center, and you got the series of major encirclements that capture the imagination (and lots of Russians). Then, in August, Hitler notices that things in the Ukraine aren't going well, and orders Guderian to head south, which he very reluctantly does, and captures half a million prisoners and he whole Ukraine.
It's not a planning change, but a better idea than what actually happened would be to then ignore Moscow and send Gunderian towards Stalingrad. But just about all the German generals thought that they just needed to take Moscow and Soviet resistance would collapse, and Hitler went along with their advice. That (and other such affairs) was why he later doesn't trust generals, like in the famous Downfall scene (not that Hitler wasn't responsible for a host of strategic blunders on his own). Of course, after the war, the US Army let Halder write the official history of the war in the east, and he shifts all the blame to Hitler, and lies about the Heer's complicity in genocide. Jerk.
Basically, Barbarossa went about as well as could be expected. Better planning for winter clothes and such could have helped, but there would still be logistics issues getting it to the front—really, the whole shebang was running on a shoestring.