This is a very interesting, if somewhat complicated question to answer. I'll do my best to keep it from veering into a History-What-If scenario. In short, we have a basic understanding of what Lincoln's intentions, if not plans, were for what we now term "Reconstruction." To define our terms, let's start with a period of focus, which generally boils down to 1865 - 1877 (The Compromise of 1877 usually signals the end of this era, and is generally accepted as such).

Lincoln didn't write much prior to his death to signal his intentions regarding Reconstruction. About the best we have is the recollections of Grant, Porter, and Sherman, who spoke with Lincoln at length over the course of about 2 days in late March 1865 (on the River Queen). This was the meeting that informed Grant et al of Lincoln's basic intentions as it concerned the surrender of the Confederate armies in the field (which was more or less imminent at that point). Lincoln signaled his plans to kinda take it easy on the south so as to foster an easier reunification. Lincoln told his commanders that if the Confederates simply laid down their arms and went home, Lincoln was prepared to leave it at that. The nature of these terms is seen in Grant's handling of Lee a few weeks later, which Lincoln approved of (soldiers just had to turn in their guns, swear loyalty to the Union, and go home - officers could keep their sidearms, and soldiers that brought their own horses could take them home).

In this, and other moves Lincoln made before his death, you can see a guy trying to put the country back together with as little drama as possible. He had already installed pro-Union state governments at the local level that required only a 10% vote to return it to the Union and get civil services going again, so I think you can sort of infer that his intention was to just start things up like nothing had ever really happened, and sort of lull the former Rebels into taking up their old lives again.

Of course, this doesn't account for what was to happen to all of the emancipated slaves, who certainly couldn't go back to life as it had been, but Lincoln's earnest efforts to get the 13th Amendment passed kind of speaks to this. Lincoln was a guy who believed in the Union and the Constitution with every fiber of his being. He probably thought that slavery, henceforth abolished by the 13th Amendment, would die like a plant without water, and that that would be that. Of course, it's impossible to know with any real certainty what he really thought (or if he foresaw Jim Crow-like legislation on the horizon), but it is at least a peek into what he thought or may have been thinking.

Beyond this, it is hard to know with any certainty without getting into speculation. Johnson's moderate policies might have been very much in line with what Lincoln had in mind, yet not being Lincoln, Johnson had a tough time with the radical Republicans, who wanted to push a much more aggressive, some might even argue vindictive, line. One has to figure that Lincoln would have had more success angling his party to get the desired results he was looking for, but again, it is hard to know how much sway he would have held in a 2nd term and without his ability to use his wartime authority.

[Sources - Jay Winik, 'April, 1865'; Bruce Catton, 'A Stillness at Appomattox"; James McPherson, 'Battle Cry of Freedom']