After the fall of Forts Henry and Donelson the two main rivers in Tennessee became invasion routes. The Cumberland River snaked east towards Nashville and thus did not offer the Union much of a campaign because Nashville soon was captured. The main option in that area was to advance southeast from Nashville along the railroad to Chattanooga. The Tennessee River though went straight south past the Tennessee state line and then continued east, roughly paralleling the state line, to Chattanooga. Near the bend of the river the Union would be roughly 20 miles from Corinth, a strategic rail junction. The capture of Corinth would almost ensure the fall of Memphis and thus begin the opening of the Mississippi River. Control of the Mississippi River was important to both sides and in early 1862 the Union was beginning its efforts to bring it back under control. Once Memphis is captured the next big defensive area is Vicksburg so the capture of Corinth means that the northern half of the Mississippi River can be brought under control pretty easily.
Once the Union decides to make a campaign for Corinth they need to select some place along the Tennessee River to begin this campaign. The Union could have picked a few other places along the Tennessee River for their camps, most notably Savannah. The high water at the time limited the places where the Union could encamp an army. The main options were Pittsburg Landing, Crump's Landing and Savannah. Most of the other landing areas up river, such as Eastport, were pretty much flooded. Once the Union was ready to advance against Corinth if they were starting from Savannah the Confederates could have tried to contest the crossing of the river. Being on the west side of the river would allow the Union an easy start but left them open to attack. Grant and CF Smith did not think the Confederates would come attack them so it did not matter to them which side of the river the army was camped on.
If the Union had chosen Savannah there would have been no battle at Pittsburg Landing. The Confederates could have attacked an army positioned at Crump's Landing because it was on the west side of the Tennessee River. To attack Savannah the Confederates would have had to cross the river which would have been very difficult due to their lack of a naval presence in the area. The Union navy would have been able to disrupt the crossing of men and supplies before the battle and been in a position to wreck havoc with any retreat.
These are critical decisions in a very simple way, the location of the battlefield is very critical to the course of the battle. A battle fought at Crump's Landing or Adamsville would certainly have been fought differently than Shiloh was. Other Peach Orchards and (slightly) Sunken Roads would have become famous. But the Union has also made a big decision here in what their objectives will be for the foreseeable future. They could have gone after Chattanooga next and sent Grant to help Buell. They could have gone straight into Alabama. Instead the Union decides that control of the Mississippi River is very important. They also decide that rather than attack Memphis from the river they will force its fall by taking Corinth first. There will be a naval battle at Memphis but that's more of a last ditch effort to save their city, there as little doubt that Memphis would fall now.