Hitler had always planned upon conquering and colonizing Russia, as can be seen in his book, Mein Kampf. Stalin had always planned on invading Germany and the rest of Europe. It was not a question of if there would be invasions. There was only a question of when and how the invasions would occur. After the deeat of Goerings Adler Tag campain in the battle of Britain, Hitler found it necessary to consider the problems he would face with a longer and more costly campaign to invade and conquer Britain, when Hitler’s intelligence services were telling him how Stalin’s preparations for his own offensive against Geermany and Eeurope were approaching readiness.
With the benefit of hindsight, we now know Stalin’s plans were doomed to failure due to the poor combat performance of the Red Army and Stalin. But Stalin was not ware of this incapacity to perform in 1941. Just as he vastly overestimated the capabilities of the Red Army in its campaign against Finland in 1940, he had no clue how bad the Red Army would actually perform in Operation Barbarossa.
Hitler decided he could not afford to have Stalin attack him in the ear while he was drawn into a prolonged campaign against Britain in 1941 or 1942. Instead, he gave the Kriegsmarine the mission to starve Britain into submission with a submarine offensive and blockade, while the Whermacht disarmed and defeated Russia. Hitler badly needed resources to continue a prolonged war. Russia and the Middle East had those oil and other resources, while Britain did not. So, Hitler trusted the Kriegsmarine to handle the threat in the Weest, while the Wehrmacht conquered the threat and the future resources in the East.
Without the United States actively engaging the Kriegsmarine in the Battle of the Atlantic, Britain had absolutely zero chances for surviving much beyond late 1942 to late 1943. Eveen with the support of the United States, the Battle of the Atlantic was being lost until 1943, when the loss rates were suddenly and deecisively reversed. Prior to a date in 1943, the Allies were losing more merchant ship tonnage than it could build by a substantial margin. If things had kept on going the way they were, Britain would have been starving to death by late 1943 to early 1945. The cross channel invasion and strategic bombing campaign in the ETO would have to have been canceled or greatly reduced. The new anti-submarine efforts of the U.S. 10th Fleet and the Royal Navy reversed looming defeat into the steady and inexorable destruction of the U-boats. Hitler could have built far more U-boats and crews before he invaded Poland, but he miscalculated the Allied response. So, the Kriegsmarine went to war unprepared to blockade Britain and starve it into submission and surrender before the United States could intervene with its entry into the war. Hitelr could still have defeated the successful Allied anti-submarine campaign by the earlier construction of the advanced design U-boats in quantity, but he chose not to do so in time and numbers to overcome the Allied successes in 1943. Hitler failed to anticipate these events when he made his 1941 decision to proceed with Operation Barbarossa.
You are quite right. The Nazi plan was to move East, as seen in MK.
Hitler never wanted to fight UK. He actually wanted to make peace after the Battle of France, leaving UK free to dominate the rest of the world while he took Europe. He assumed, not unreasonably, that the Brits would make peace after such a total defeat. He was absolutely shocked when they gave no sign at all of interest in peace.
From the POV of Nazi ideology, fighting in western Europe at all was a diversion from the true German destiny in the East.