I use an OpenOffice Calc spread sheet to keep track of building; pencil and paper *psss* how 19th century

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I start out by entering all the units I have on the map and add those that I get and build. It's organized into sections; one for each theater.
When I have units that I want to use to build a division I drag-n-drop them together (yes, you can do that in OO Calc - I have a special military-map font installed, so nearly all element types are represented and can actually enter the units into a cell so that they look like in the Inspector Panel, only horizontally stacked and not vertically) and then check what I have and what I might still need to build.
When I plan to build a division I first check what units I have available and drag those I want together. Then I check what units I can build and enter those I want to build.
When I build a unit, once I've dragged it on to the map, I enter it's name, build date, days-to-build, build location and constituency into the spread sheet and mark it with a red background. The spread sheet calculates when the unit should be completed. This way I can always see when a division will be ready for the front and what would be missing if I sent it early.
When a unit is completed, I give it movement orders to where it will be put into a division and mark it yellow in the spread sheet; when it's built into a division it's marked white.
What should you put into a division? Numerous, long threads have had that as their subject. What I can say with confidence:
1 sharpshooter per division (
always)
1 elite unit with at least 1 element with the Strong Morale attribute (practically all of them have at least one), if I have one available (more than one per division is a waist)
1 10 lb battery (I've never really tried more)
3-4 6 lb and/or 12 lb batteries (I generally don't worry about any mix of these and am generally happy to just use those 6 lb-ers that come with units; after these units are used up, or when the unit mix forces me to do so, I start to buy 12 lb-ers directly)
1-2 cavalry (never build a division without at least 1 or else it will be in grave danger of having elements pursued and destroyed if it breaks in battle)
the rest is infantry filling it up to 17 elements, plus 1 leader
Early in the game I build nearly every unit in one of the following cities: Philadelphia PA, Cincinnati OH (Dayton OH if I haven't invested in Armories in the Mid-West, which you need for artillery), Springfield IL with a few in Washington and Saint Louis, depending on what I need. I try not to build too close to the front that the units in training might get attacked and destroyed before being completed, but not so far as that it takes more than 1 turn to get to the front by rail.
This works well until about '64 when, if Richmond has been taken and the South hasn't collapsed, as the Union the front will probably have move beyond 1 turn's travel from your build locations in the East as you will be building in New York and New England. More than 2 turns distance, and you're just toying with the South like a cat with a mouse
In the West it's a different story. Once you've taken Springfield and Fayetteville no matter where you build it will take a while to get units to the front. You'll be building in Michigan and Wisconsin and may have to use transports to get units to where they are needed quickly.
For the Gulf coast I nearly only build units in New York City. NYC has the quickest route to New Orleans and the Gulf Coast.
For the Far West... the best you can do is send one of the leaders with Training Master to train up the militia unit you can build there. Once one has been trained up to Line Infantry, the militia unit is returned to the build pool and you can rebuild it. This is quicker than trying to send them in from anywhere else.
Since I use the spread sheet for planning my divisions I don't have to worry where I'm building so much. I just look at my build plan and I know where the units are being built, or when a message appears in the mail box that a units build has completed, I can check to which division it belongs and send it on its way.
I can put up a copy of my planning spread sheet if anybody would like one.