I am inexperienced in Unity. I knew this going into this project. I disregarded everyone's advice to avoid learning new tools going into a Ludum Dare. Why? Because I learn VERY well in this sort of environment. This kind of pressure seems to help me stay focused.
So I whipped up a player sprite with full movement animations in one hour. Then... I spent the next five and a half hours in Unity getting it to move and animate properly. But, in the end, I pulled it off, and I'm thrilled! I'm also really fatigued, and it's bedtime.

The most interesting challenged I faced with this little dude is how to determine which direction he should face when moving diagonally. Originally he was defaulting to whatever the highest priority facing on the list was, which generally meant he would always face up or down when going diagonal. Then I took care of that, but he would instead start rapidly flickering between the vertical and horizontal animations when going diagonally.
In the end, I set it so his direction only changes when he is only moving along one axis. If you're moving right, then start moving diagonally up or down, you keep facing right. If you're moving down, and you start going diagonally left or right, you still face down. Perfect.
But what if you start going diagonally at the same time? The character was having an awkward moonwalking effect when doing that. Ah, gotcha. Now I can choose which direction to prioritize! Here it now defaults to horizontal facing.
Still have one little issue: the sprites on my sprite sheet are too close together, so sometimes, due to the way Unity is scaling my sprites, I'm getting little black lines above his head that look like the bottom of his feet. Whoops. That should be an easy enough fix, but I'll deal with that tomorrow.
I guess tomorrow I also need to start making the game itself. Oh shoot, let's not forget that part.