Lincoln is known to have made statements consistent with the prejudices of many white northerners at the time. Here, for example, is an extract from his 4th debate with Stephen Douglas:

"I am not nor ever have been in favor of making voters or jurors of negroes, nor of qualifying them to hold office, nor to intermarry with white people; and I will say in addition to this that there is a physical difference between the white and black races which I believe will forever forbid the two races living together on terms of social and political equality. And inasmuch as they cannot so live, while they do remain together there must be the position of superior and inferior, and I as much as any other man am in favor of having the superior position assigned to the white race. I say upon this occasion I do not perceive that because the white man is to have the superior position the negro should be denied every thing. I do not understand that because I do not want a negro woman for a slave I must necessarily want her for a wife. My understanding is that I can just let her alone. I am now in my fiftieth year, and I certainly never have had a black woman for either a slave or a wife. So it seems to me quite possible for us to get along without making either slaves or wives of negroes. I will add to this that I have never seen, to my knowledge, a man, woman or child who was in favor of producing a perfect equality, social and political, between negroes and white men."

Lincoln fell into a category of people we could broadly call antislavery in the sense that he they opposed the expansion of slavery into western territories, didn't particularly like it, but also were not in any great hurry to take immediate action against it. Lincoln is also known to have at different point advocated for what we call "colonization," a family of antislavery ideas that had as part of its program the settlement of freed slaves outside of the United States. This is one of the reasons the nation of Liberia exists, though other destinations in the Caribbean and Central America were at different points considered as well. Lincoln's views on race and slavery were well within the mainstream of white northern opinion of the time. Support for immediate abolition of slavery and full racial equality was minority position even after the outbreak of the Civil War

Readings

David Herbert Donald's Lincoln is still the main go-to biography of Abraham Lincoln. For a shorter, more politically-oriented biography, see Richard Carwardine's Lincoln: A Life of Purpose and Power.

There were definitely multiple glaring moments from the 1800s where Lincoln showed some prejudice against black individuals. One that I'd like to point out is a situation that often gets overlooked, especially in school curriculum. There was a period of time where Lincoln tried to get Africans and African Americans to move out of the U.S and to their own "colony" elsewhere. Here is a source containing information and some of Lincoln's own words about the colony idea. There's a lot to it, but I'm going to insert a couple of quotes and break them down.

The first quote: "Your race are suffering, in my judgment, the greatest wrong inflicted on any people. But even when you cease to be slaves, you are yet far removed from being placed on an equality with the white race. You are cut off from many of the advantages which the other race enjoy. The aspiration of men is to enjoy equality with the best when free, but on this broad continent, not a single man of your race is made the equal of a single man of ours. Go where you are treated the best, and the ban is still upon you."

Here, one can see that Lincoln isn't necessarily spouting hate against black people, but he isn't fully supporting them either. Lincoln argued that blacks and whites were unable to peacefully live together because they were considered to be too different (lacked advantages that white people had). He also thought that even if enslaved individuals gained freedom, they would never be treated equally when living around their former enslavers and other white descendents.

The second quote: "It is better for us both, therefore, to be separated. I know that there are free men among you, who even if they could better their condition are not as much inclined to go out of the country as those, who being slaves could obtain their freedom on this condition. I suppose one of the principal difficulties in the way of colonization is that the free colored man cannot see that his comfort would be advanced by it....But you ought to do something to help those who are not so fortunate as yourselves. There is an unwillingness on the part of our people, harsh as it may be, for you free colored people to remain with us. Now, if you could give a start to white people, you would open a wide door for many to be made free. If we deal with those who are not free at the beginning, and whose intellects are clouded by Slavery, we have very poor materials to start with. If intelligent colored men, such as are before me, would move in this matter, much might be accomplished."

Now you might get a better idea at how direct Lincoln was with the idea of sending anyone who was black- enslaved or free- out of the U.S to try and create this sense of peace among the white people who were divided on whether enslaved individuals should have been freed. Lincoln didn't even have a clear idea of what could happen to the people of color he thought should leave. Take the last sentence I quoted; what could Lincoln have possibly expected when he said "much might be accomplished?" He clearly didn't think the same could be done if black people and white people lived together. That shows his prejudice and bigotry, and even though he wasn't blatantly racist like many of the white southerners, Lincoln wasn't exactly a saint when it came to emancipation and trying to end the divide between races.

Oh, and if you're wondering, colonies were created in Africa, and people were sent there. Liberia was one of them from the 1820s to the late-1840s before it became independent. Lincoln was well aware of the colony and continued to support the deportation of Africans and African Americans to that colony. From what I've read in the past, this process was largely abandoned because people kept getting sick in the colony and it wasn't successful.

TL;DR: Lincoln showed his prejudice, racism, and bigotry by supporting the idea that black people should be sent to colonies outside the U.S because they wouldn't coexist with whites in the U.S.

Edit: I just saw the comment from u/CrankyFederalist below and saw they brought up the colonization idea. I'm glad someone else knows about this and was willing to mention it. I guess my comment is an expansion of that.