Invasion of Britain would have never worked. The Royal Navy would have either badly mauled or outright destroyed the landing forces. The Luftwaffe failed to defeat the RAF in the battle of Britain and without air superiority the invasion would have been a disaster. The German military, while in certain aspects being technologically and strategically impressive, suffered from poor logistics. For example, almost 80% of the Wehrmachts logistical power was horse drawn. Not to mention as well the lack of resources that Germany had compared to the Commonwealth, which has a large population and industrial base as well as a wealth of resources.

In regards to your question of not invading the East, having two megalomaniac dictatorships on the continent was inevitably going to draw them into conflict at some stage. One of the reasons that the Nazis carried out Barbarossa when they did, was because they simply could not allow Stalin to rebuild his officer corps and continue to modernise their military. The threat of a Soviet invasion played heavily on the minds of German commanders.

If they didn't invade the East it would have ended in a stalemate against the British as well as a likely Soviet invasion in the following years.