It's almost impossible to separate Lincoln from the slavery issue because it was the all consuming national drama of the preceding decade. However, it was not the only thing that was going on. We should also note that at the time the president really didn't do much legislating -- he just sort of sat back and waited for Congress to send him bills.

If we go with your counterfactual that the South didn't secede then we do have a series of public statements from Lincoln about what he was going to do. His main policy, and the thing that actually caused the South to secede was that he was not going to allow slavery to expand. As he said himself, he was a "convinced anti-slavery man" but he also, in accordance with the main legal doctrine of the time, believed that slavery existed in state law only as a protected institution. He planned to use the power of the federal government to ensure that slavery would not expand any further into the territories. This unflexible stance is clear in both his personal and public statements. For instance in a letter to Lyman Trumbull after he won the presidency but before he was inaugurated he said "let there be no compromise on the question of extending slavery,” and he was determined not to be blackmailed by the South. In a different letter to the Pennsylvania congressman James T Hale he said either attempting to play upon us, or they are in dead earnest. Either way, if we surrender, it is the end of us, and of the government... a year will not pass till we shall have to take Cuba as a condition upon which they will stay in the union” ” However, while he did not want slavery to expand he wanted all relevant laws to be obeyed, even ones which northerners disliked such as the fugitive slave clause. For instance in a letter to Thurlow Weed “also that I probably think all opposition real and apparent to the fugitive slave clause of the constitution ought to be withdrawn." These statements were in perfect harmony with his stated views in his speeches. In his Cooper Union Address, for instance, he set out his constitutional and legal views on the slavery issue that “the federal government however, we insist, has the power of restraining the extension of the institution.”

While slavery took up the entirety of the political oxygen, there were still other issues at play which Lincoln and the Republicans were interested in. The Republicans, as the successor party of the Whigs, were still interested in debating political issues stretching back to the 1830s, for instance about how much money the Federal Government could spend on "internal improvements" As such, the Republicans offered in their manifesto of 1860 "That appropriations by Congress for river and harbor improvements of a national character, required for the accommodation and security of an existing commerce, are authorized by the Constitution, and justified by the obligation of Government to protect the lives and property of its citizens," as well as plans for a trans continental railway (passed as the Pacific Railway Acts of 1862 and 64). Another major issue was that of land in the west. This again found its way into the platform of 1860 as a call for a Homestead Act, which was eventually passed in 1862 and provided settlers with 160 acres of land if they agreed to move out west. There were other sundry bits and pieces, but Lincoln's political identity from the moment that he gave the Lincoln-Douglas debates was defined by slavery. After his election he became a war president and really didn't have the time to do anything much after that.