I've decided to use Minecraft like characters in my small game since I do not know how to make 3d models (nor I want to learn how to do such thing in the near future).
However the task now seem a little harder than expected: I've tried looking in the asset store for prefabs to use but without success. So, I've decided to try and make a model on blender(by not knowing a thing about non parametric 3d modeling, my knowledge of blender is extremely limited) and import it into my unity game. And surprisingly, I managed to create the model using McPrep, export it and import it into unity maintaining objects that drive the bones (the output is a bit messy but I think I can manage to clean it up a little). However the imported version does not have any skin and appears in a gray shade. Turns out that the output does not keep materials/textures with it!
I've tried getting the texture used by blender and it returns the same skin I fed into mcprep so, by using the same skin, I've tried creating a material with it by getting the .png and using it as texture in a unlit texture material. However, the result is a bit messy as shown here (left is Blender, right is Unity):

How may I make the texture on unity3d be better and right? (I've heard there is a way using a C# script but I really don't know what it is nor how to do it)
EDIT:
Thanks for the answers before, I did set the filter to point obtaining the texture to be a bit better. However the part that should be transparent is displayed in black on top of the other part (I think).
The image on the right is only filter point and the one on the left is point + alpha is transparency and the transparent shader using unlit transparent

You're running into a filtering issue. In your case you want no filtering to happen. So select your texture, and in the inspector change the import settings so that your "Filter Mode" is set to "Point". In this case it will do no filtering of the input and your large pixels should appear sharp as you want.
As Bart said, make sure the textures' Filter Mode is set to Point, but additionally:
Minecraft player characters are made of 2 layers, the second layer usually has lots of transparency and is used for clothing or other relief detail. So you need to use a transparency-capable shader on your material in Unity.