I realise it's quite a broad question.. but could someone try and explain what considerations went into planning the war at a strategic level?
In my reading, I see river-control come up a lot. What was involved in controlling a river? Was there more to it than just controlling the cities on it, and using them to base your gunboats out of it? Also was the main reason just to control it as a quick supply line (how much faster than land-based supply is river-based supply?) or also to deny the enemy crossing it with an army (or is it too easy to just blow away a couple gunboats and send your army across even without controlling it?)
The cities that became focal points, what made them focal points? Were they all just transportation hubs, or were there other reasons an army might think "we better take this one" or "we better fortify this one"? In the 1860s was being an industrial centre that big of a deal, or were factories rudimentary enough that it was easy to just pop a new one up elsewhere?
Thanks
I'll do my best to answer the questions you laid out, but they jump around a bit, so forgive me if I miss a few points (feel free to follow up with questions about what I missed). So, to start with your initial question from the title, what would a general have to keep in mind when planning a theater strategy. Well, except in a few cases (and this was generally early in the war), generals didn't really map out the broad strokes of theater campaigns: the presidents did. By and large, it was Davis and Lincoln, working with varying degrees of input from their cabinets, that did this sort of planning. There were obvious exceptions, as Lee was given a lot of freedom to suggest campaign strategy (his expeditions into Maryland and Pennsylvania were more or less his plans), and the generals of the Army of the Potomac did indeed plan many of their big campaigns (McClellan planned the attack up the peninsula in '62, and Burnside planned the disastrous advance on Fredericksburg), but this was always conditional on the approval of the president (north and south).
Now, the thinking behind what was important and/or the primary objective of a campaign varied as well. As the war went on, Lincoln, Grant, and some of the other more forward-thinking leaders of the time began to understand that what mattered wasn't the taking of cities, per se, but the destruction of armies and the enemy's ability to continue prosecuting the war. So to again go back to your question (what were the planners trying to "do"), this changed over time. Early on, Lincoln focused on keeping border states like Missouri and Kentucky out of the Confederacy, and positioned armies out "West" to check the advance of southern mobilization and movement in those regions. It was thought to be important to control the major industrial centers of that region, as well as to lock down and control the transportation network composed of the rivers and railroads out there. This was indeed a valuable consideration, yet as time went on, it became clear that to end the war, the Union had to destroy the Confederate armies in the field, so the focus shifted to finding the enemy, and routing him.
The focus was different in the south, however. When it became clear that Lincoln would never compromise over the issue of the Union's dissolution, the focus turned towards European recognition and turning opinion against the war in northern cities. To this end, Lee and Davis' strategy hinged on making a good show of things in the north (i.e., making the north look like it couldn't defend its people and cities). What the south was looking to "do" was largely built around 3 considerations: (1) going into enemy territory to gain supplies and provisions that were exhausted at home; (2) to demonstrate southern military prowess; (3) to scare the north into making peace. Early on, it was clear that the south wasn't going to win via conquest, the best they could hope for was to wear down the north's commitment to seeing the conflict through, and convince European powers that it was in everyone's best financial interests to mediate so as to stop the war and get regular business going again.
So, in the north, what they were trying to "do" early on was to put a lid on all the different secession leaks sprouting up and keep what territory they did have in Union hands. As time went on, the strategy shifted into a sort of dismemberment strategy: divide the south into segmented, isolated pieces, and destroy it fragment by fragment. This was accomplished by taking Vicksburg and regaining control over the Mississippi (effectively cutting the Confederacy in half), and in routing all the different armies until the south's fighting forces were disbanded. In the South, the idea was to hold fast while on the defensive (draining Union army roll calls), and take advantage of opportunities to invade "border" territories like Pennsylvania and Maryland to get supplies, new recruits, and generally make the north look like it couldn't handle its sh*t.
To answer your question about river supply lines, they were indeed very important. Roads could (and often did) get muddy, making it difficult to move artillery pieces and wagons, so having deep draft rivers could be a God-send. When it came to controlling rivers, this hinged on a commander's ability to take the forts that usually guarded the crucial turns and bends along the way (no small task if the fort was designed, manned, and supplied properly).
As far as what made cities focal points, this usually had a lot to do with either industrial concerns (i.e., the city had an iron works, or a boat yard, etc) or as a transportation hub that served as a concentration point for many different roads. In the 1860s, having an advanced industrial center was indeed a big deal, and not something that could easily be replaced via a quick construction of a new factory.
[Sources: James McPherson, "Battle Cry of Freedom"; Jay Winik, "April, 1865"; Bruce Catton, "Grant Moves South" & "Grant Takes Command"]