My wife, who grew up in the Chicago area said all she learned about it was "There was a Civil War. We won. The slaves got freed." End of story.
I always find it interesting how few people know the real cause of that war. The real cause had to do with changing economics and the differences between the economies of the North and South. This resulted in disputes over tariffs on imported goods which in a nutshell can be summed as the north being Pro-Free Trade and the south being Pro-Made in America. The honest truth is that the entire freeing of the slaves only got added at the end, it almost was something where the North said "Hey we won, so free the slaves too."
Anyway back on the OP:
Given 15 days to train the army and equip them with small arms.
Day 1 is testing, throw rifles at the troops and see what they do.
-Very Good shots (those that shoot well, and adapt well) get an M1 Carbine or M14 with Semi-Automatic Fire only.
-Average shots get the M16 in M4 configuration, these will still out shoot the muskets in range and accuracy. Maybe a few of them who display good presence of mind get an M204 launcher under the barrel.
-Guys that appear nuts (Rambo types) and those that can't hit the broad side of a barn get a mix of Shotguns and M249 SAW Machine Guns.
For non-infantry units
-Artillery soldiers get 1911 Sidearms in .45ACP
-Cavalry units get the Mosin-Nagant with Bayonets.
Day 2 thru 5 is individual training on their own weapons
Day 5 thru 10 is unit training, shooting together
Day 10 thru 15 is army training, multiple units coordinating efforts
Oh and one last thing: We go across the ocean and draft Napoleon to command the artillery units.