Ok, I've seen some pretty amazing and pretty horrible textures thus far:
I will share my knowledge with you.
I want to flatten out a firm understanding as to how each texture type works:
Note on Texture Size:
It is advisable to use powers of 2 when making textures, e.g. 32x32 pixels; 64, 128, 256, 1024, 2048 etc.
note: going above 2048 is unproductive as it wastes memory and is generally not necessary, unless, you're making one hell of a large object.
Procedural textures are at least a usable option in this area(maybe not the best looking)
Note on model UV's:
Do NOT use a large texture if the UV only fills up half of the space, instead use a texture half the size and FILL the whole UV space up to the best of your ability.
Diffuse Texture: A diffuse texture is the *Base Colour for a 3d model, it is affected by ambient light, specular and shine.
Application: You will want to use a diffuse map for basically all custom textures you create.
Specular Map: A specular map is one that allows specular light(shine) to be shown at different intensities according to a dark/light scale, e.g. the lighter parts of texture will reflect light, the darker parts will not.
Application: A specular map can make or break the model, it should accompany most materials, such as a metalic diffuse for example; if it has dirt and is like most metal it is not entirely reflective like chrome and will therefore have parts which do not reflect light.
Transparency Map/Opacity/Alpha: This map can be used in rendering or in-game to allow different areas of the model to appear transparent(see through).
Application: If you want to make a low poly fence ingame, then making every deatil in polygons is just not feasible, therefore an alpha map would give a realistic look as it would create the holes in the fence in the texture, bot as polygons.
Normal Maps(Tangent Space Normals): A Normal Map is created by either passing a greyscale heightmap through a normal map converter or baking a high poly model onto it's low poly versions, normal maps create a vast improvement in detail by giving the illusion of depth and indents etc.. It works by tricking the renderer into bouncing light in a way that does not conform with the low poly, basically it projects the details of the high poly model onto a low poly.
Application: Normal maps where applicable are an industry standard way to add detail to ingame objects at no expense to framerate compared to if you had the high poly version ingame.