My specialty as a historian centers on Civil War Medicine, but I have a general interest in the era - so feel as though I'm reasonably equipped to provide a brief answer.

Eric Foner's Pulitzer Prize winning book The Fiery Trial deals with Lincoln's personal views on slavery throughout his life - and it is from this book I am basing my answer.

Lincoln was not an abolitionist in the true sense of the word. He did not advocate the immediate emancipation of the slaves. You are correct that Lincoln believed slavery was morally wrong. He also believed that eventually slavery should/would end (his famous 'House Divided' speech lays out this theme). However, Lincoln's background as a lawyer meant that his moral unease with slavery was at odds with his respect for the law and the constitution that protected an individual's 'property'. Since slaves were property, simply the government could not seize them and rule them free as this would be large-scale theft.

Foner outlines a number of Lincoln's various ideas for solving the problem of slavery. Lincoln was a supporter of Recolonization (the idea to promote voluntary emigration of slaves and freemen to Africa or the Caribbean). Another plan of Lincoln's was that any children born to slaves could be made free and that eventually slavery would die out on its own (with a final deadline for this put at 1900).

Going back to your question again, your point on why Lincoln and the North went to war could be a whole answer in itself. However, for simplicity's sake I'm going to agree with you (and Foner's argument in The Fiery Trial agrees too) that Lincoln's primary goal in the Civil War was to preserve the Union.

Foner is keen to point out that Lincoln was reluctant early in the Civil War to free the slaves since he was concerned the remaining loyal Upper Southern states would secede if he introduced this measure. Lincoln's issuance of the Emancipation Proclamation on September 22, 1862 (coming into effect on January 1, 1863) was a war measure to undermine the Confederate States since - to quote the proclamation - the order only applied to "the people whereof shall then be in rebellion against the United States" and not slaves still residing in loyal Unionist States.

I don't want to go any further with this answer as I am not so well-versed on the circumstances leading up to the 13th Amendment (perhaps someone else can fill in my gaps?).

So in summary, Lincoln's views on slavery were forever changing and adapted to the political situation around him. Foner argues that this tendency for evolution and compromise was perhaps Lincoln's greatest political asset. Lincoln was never an abolitionist of the same vein as Charles Sumner, Thad Stevens or William Lloyd Garrison. However, his moral distrust of the institution of slavery was a key factor that lead to the Emancipation Proclamation and 13th Amendment.

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Sources:

Eric Foner's The Fiery Trial: Abraham Lincoln and American Slavery

Bruce Levine's Half Slave and Half Free: The Roots of Civil War

and double-checking dates and quotes on Wikipedia.

edit: spelling and grammar