There are whole shelves of books dedicated to unique and exotic weapons of the Civil War, but one area that seems to receive less attention is the least expensive models. With the advent of mass manufacture and the need to arm and equip hundreds of thousands of men, what was the cheapest firearm to produce? What firearm showed up the least for repairs? What did soldiers in the field prefer for its simple design?
For guns purchased in big numbers, rifled muskets were definitely cheaper, cheaper to supply with ammunition and more easy to service than breech loading guns ( which maybe is what you mean by "exotic"). According to the Ordnance Dept's statement of purchases from 1861-1866, certainly the few million mostly Austrian rifled muskets imported by Herman Boker & Co. for the US War Dept. were cheaper than the more standard Model 1855 or 1861 Springfield rifled muskets. Springfield was deep into its quest to produce guns with interchangeable parts, and it came at a cost: each Springfield cost the Ordnance Dept $19.52. The "Lorenz" rifled muskets were more varied in quality, fit and finish, and were around $13. I say, "around" because they first came with fixed simple sights that didn't allow change of elevation, and had to be reamed and rifled from .54 caliber to .58, if they were to take standard Springfield ammunition.... and I am not sure how and when all that was applied to the cost. One auction house website says that the ones fitted with the improved Enfield leaf sights were $15: but I don't know their sources ( though some collector has no doubt done an exhaustive work on the history of Lorenz rifled muskets, I don't have it). But the more expensive Springfield musket , with more interchangeable parts, would have been easiest to service. If a Springfield needed a new lock, it could be simply screwed into place, while a new lock for a Lorenz ( assuming one was available) might first need some fitting by an armorer. That was, of course, the idea behind interchangeable parts.
Along with buying millions of Springfields and Lorenz muskets, the War Dept. discovered that, like buyers of cell phones and computers today, the best deals were for the stuff that was out of date. They also bought thousands of miscellaneous old guns, some already in the US and some that were being dumped out of foreign arsenals at good prices. The Prussians had been winning wars with their Dreyse needle guns, and so it was to be expected that they would sell 81,652 very obsolete " smoothbore muskets" to the US for just $6.80 each. The Model 1839 Potsdam musket was .72 caliber and could have used the same buck-and-ball loads that soldiers sometimes used in the .69 caliber Model 1842 Harper's Ferry musket. But I don't know who got them, and if they were happy to have them: the German and Austrian guns often came with beech instead of walnut stocks, which added some weight for the soldier to carry on his shoulder. And if that shoulder had been feeling the repeated recoil of a .69 caliber buck-and-ball load, it might have been already a little sore.
The muzzle-loading rifled muskets were cheaper to buy, cheaper to supply with ammunition and easier to service , but the ultimate economy was to raise the rate of fire per soldier. Even in 1859 the Secretary of War would note that a soldier with a good breech-loading gun would be the equal to two, possibly three soldiers armed with muzzle-loading muskets. If one breech-loader cost even twice as much as a muzzle-loader ( a Sharps rifle would be $36) that one soldier would consume much less materiel than two: need only half a tent, eat half the rations, wear out half the boots.
Fuller: The Breechloader in the Service