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The best reading for this question (as with any on Reconstruction) is Eric Foner's Reconstruction or the abridged A Short History of Reconstruction. Both are very readable. But since this is such a huge question, any answer here is going to have a lot of generalisations and points to challenge. But I'll answer it to the best of my ability.
Between Congress, the Presidency, southern Democratic (generally former slaveowners), and southern Republican (the so-called 'carpetbaggers', 'scalawags', and, from 1857, freedmen), there wasn't any single approach to economic policy in the South. So there are a huge number of actors with power to shape aspects of economic policy, and these change over time. Also remember that there wasn't a consensus on economic policy in the North either, between protectionists and free traders; paper money advocates, silver activists, and greenbackers; and nascent labour activists and a growing bourgeoisie. (If you want to read more about these people, go for Sven Beckert's Monied Metropolis, but it's a little dense.)
At the start of Reconstruction the federal government does have some experience in dealing with some of the economic aspects of Reconstruction in southern Louisiana and occupied islands off South Carolina. However, the military is generally given a free hand to settle these questions as it likes on the ground, and local officers do what they can based on local needs. Banks and Butler in New Orleans do this by trying to put slaves (and they are still legally slaves right up until the Thirteenth Amendment) back on sugar plantations, in South Carolina the planters have fled so the Union lets freedmen generally farm as they like, and in Georgia and South Carolina Sherman and Sheridan assign freedmen land to farm as they wish, but without any intention for this to be a permanent solution. There's no real comprehensive 'policy' as far as we would understand it other than getting the cash crop industry back on track. The Treasury Dept at this point is trying to keep itself solvent more than anything else.
However, as the shift focuses from war to Reconstruction, there is a debate between different Northern policymakers over land redistribution which shapes what the Southern economy will look like going forward. Supporters of land redistribution support seizing Southern planters' lands and handing it to freedmen to engage in subsistence agriculture, which is already a large part of the Southern economy outside of the cotton belt. This also looks similar to the ideal of the Homestead Act, which gives away plots of Western (Native Americans') land to farmers to grow their way to self-reliance. The opponents of redistribution are a diverse group, but those who don't just define policy in terms of opposition to redistribution generally envision freedmen farming cash crops for wages with their former planters as employers. This is a policy that speaks to a lot of Republicans who joined the movement in the 1850s under the banner of 'free labor', who assume that the free market will allow freedmen to save, acquire property, and eventually acquire land by themselves just as Northern factory workers can save and eventually become propertied artisans. In theory. Despite the so-called 'Radical' phase of Reconstruction after 1857, land redistribution never happens, though South Carolina has a good go. However, the wage system never takes off either.
At the same time, you also have Southern policymakers. Without a great deal of federal direction this is left to the states themselves, but there are similarities between them. Under Andrew Johnson, former slaveholders are generally left in charge of state governments, and their policy is to return back to the antebellum status quo, using state authority over black subjects rather than the master-slave power relationship. So you might say their economic policy is to return to the political economy of slavery, based on cash crop agriculture. In 1867 Congress kicks out these governments and provides for black suffrage and confederate disenfranchisement. These governments try and modernise the Southern economy, mainly by building railroads, universities, and infrastructure, and social welfare and emulating the Northern industrial boom that has bypassed the South.* This is a huge sweeping generalisation - freedmen on homesteads still grow some cotton for the market to earn cash, and planter-led governments also invest in railroads and infrastructure, but this is, I hope, a fair reflection of Southern states' economic policies in the period.
These all fail. There's no real redistribution, but there's no money for new infrastructure or the resurrection of the cotton industry either. There's no New Deal-esque public injection of capital into the Southern economy, and private capital can get better returns in the North. The Southern economy therefore just never has the cash circulating to invest in cotton or railroads, or much else. So in practice, the South turns to the barter economy of sharecropping. So you might say that, in the absence of any agreement on an economic policy for the South and political will to see it through, the most striking aspect of Federal policymaking over the South is one of neglect, even before the Federal government actively turns against Reconstruction and the increasingly active labour movement in the North in the 1870s. At this point, there's not much of a distinctive Federal-led Southern economic policy separate from the battles of the Gilded Age economy.