TanaNari, some of the criteria is about having a character who is exceptional in any way, and some of it is just about if a character has some similarity to you in any way.
He is of my gender, and we share the same skin and hair colors. He has been the same general age as me. Same sexuality. Had either the same job as me or a job I would like to have (president, lawyer, businessman, there's a few to pick from). We share a hobby (he was an avid reader). And I do think people who read a biography of Abraham Lincoln will like and empathize with him. I also have fantasized about him beating people I don't like, seeing as I don't like the Confederate States of America. It also counts if you don't like vampires.
He has a remarkable body type, being tall and slender to the extent that some think he had some unusual medical condition. He had a wart and scar over his face, though you don't really notice them. He has a unique possession on his person, his iconic hat. He looked older than he was, a trait all U.S. presidents share after spending time in office. Technically, he never has to worry about money now, but I didn't give him that one because of various issues with poverty, failing business, the formation of the Secret Service to combat Confederate counterfeiting, and audits of his spending in the White House. Often depicted in black clothing. As a world leader, had to spend a lot of time at parties.
When it comes to unusual stories about his infancy, he spent six months alone on the frontier caring for himself and his sister after his mother died and his father left to go find a new wife. Plus, his nickname "The Rail Splitter" came from his being raised on the frontier in a one room log cabin and learning to use an ax at an early age. I didn't include it the first time around, but he was raised by a parent who wasn't his biological parent when his dad finally got back with the new wife and her kids. His being from the frontier is also why he's from a different region/world than others he dealt with in Washington D.C. The U.S. in his time was unusual as a democracy, but in some ways was technologically backwards.
Was abandoned by a parent. Raised in extreme poverty. Was a member of a despised political group. Suffered terrible guilt about a lot of things, including the Civil War, which wasn't his fault, and any sensible person could see it wasn't. Was persecuted by his father for preferring reading and education. Was falsely accused of crimes by the South and the Copperheads during the Civil War. Multiple family members died tragically, including a younger brother, his sister, his sister's baby, his mother, and two of his sons, so a regular kiss of death. And he did indeed feel responsible for the death of loves ones, friends, and so on of his that died in the Civil War, though not his fault.
Everyone admires Lincoln (except the bad guys). Sometimes, other people did talk about how great Lincoln was. Characters who disagree with Lincoln over issues like slavery do indeed suffer horrible ends that prove Lincoln was right, to the extent that they might as well stock up on body casts. Lots of dead Southerners. Also known as pretty darn good at debate, winning many a verbal battle. Older and wiser heads did not want Lincoln fighting out the Civil War. The previous president made it a point to do nothing, since he felt the federal government shouldn't stop secessionists seizing federal land and armories, and the Copperheads often pushed for peace instead of victory in the Civil War. Not only did Lincoln not get pulverized, but he's gone down in history for saving the day and not facing consequences from them for disobedience to their advice. Probably because a Southern sympathizer assassinated him first, but not from the politicians. Plus, Lincoln was known for being good with animals and kids.