So, the only trick to answering this is to keep in mind that the office of the president was perceived somewhat differently in the 1860s: Lincoln and many others held to this belief that the president should not shepherd through legislation or dictate what should be passed, instead leaving it to Congress to pass laws for his review. So keep in mind that a lot of these accomplishments were the purview of the Republican party in Congress, and not Lincoln proper.

The Civil War actually sees the passage of a number of Republican/Whig/Free Soil goals that were separate from the war. In many cases, the South had operated as an obstacle to these bills or the hopes behind them, meaning that when a host of Southern Democrats leave, the floodgates opened in Congress.

One immediately obvious one is the Homestead Act of 1862. Republicans and their antecedents in the Whig and Free Soil parties had hoped for the passage of a bill that would open up public lands in the west cheaply, and this first Homestead Act did exactly that: people could apply to work a 160 acre plot of land, and if they did so for five years and made "improvements" to it, they could receive title. There's been a lot of ink spilled as to whether this benefited speculators or farmers, and for that matter how effective it was: large parts of the areas west of the Rockies are too arid for small-plot farming, leading to a great many farm failures. I'll leave the assessment of the act to somebody who's better versed in all of that scholarly literature, but in any event, the estimate is something like 600,000 farmers had received title to a combined total of 80,000,000 acres of land by 1900 (of course, there were successive Homestead Acts after 1862 that account for some of that). Even if you come down on the side of big businesses and railroads using it predominantly for speculation, it exerts a powerful influence on the history of the American West.

Speaking of railroads, I would be remiss if I left out the transcontinental railroad, which was authorized through the Pacific Railroad Act in 1862. It provided for a route that would link the east and west coasts in exchange for land grants to the railroad companies as well as government-backed bonds to finance the project. This gave the railroads incentive to build while also helping to settle parts of the country that had heretofore been too remote for most settlers to consider. This also reinforced the impact of the Homestead Acts, which in turn helped reinforce railroad construction: without people to settle near railroads (and preferably to buy up those lucrative land grants), the companies would have lacked incentive to build in the first place. This helped to fuel further railroad construction as well, because as places became settled, there was in turn demand for more access.

The first income tax is passed during the Civil War. While it's only a temporary measure that ultimately expires in 1873, it set an important precedent with the idea of a progressive national income tax that's eventually enacted into law with the 16th Amendment in 1913.

The national banking structure was also reformed by Banking Acts that tried to standardize and strengthen weak legislation around banks by requiring federal charters; this was to try and put an end to so-called wildcat banks and instead put banks on stable financial footings. Perhaps most immediately, it created a uniform national paper currency, the greenback, that could redeemed for gold and silver. This was a major step towards having a uniform currency in the United States separate from specie (previously, banks could issue their own notes that could be redeemed for gold; this meant that a whole host of paper notes proliferated from hundreds of different banks).

Lastly, there was the the Morrill Land-Grant Colleges Act, which created state colleges that would be financially supported by land grants. These were supposed to be agricultural colleges, and today they form the basis of many states' higher educational systems.