The UV map itself is dimensionless really. It's generally the accepted way to have the entire UV map fitting in the in the 0-1 coordinate range in the editor.
It's generaly not advised to use a texture-map of greater than 2048x2048, due in part to the number of cache-misses this will entail and the associated hit to speed.
It's not unusual to use several texture maps for a character, utilizing them on different parts of the body. Doom(ver?), for example, uses seperate texture maps for the head and for the body. If memory serves me correctly, they're 1024x1024 for each. Although light-years ahead of what I grew up playing, they're still not exactly super realistic.
It really depends on what the character will be used for (game/still shot/animation), and especially on how close the camera will get to them - the number of pixels the character will take up on the screen in the final render.
Alex Alvarez has written an excellent article on Texture Resolution which is well worth a read and highly reccomended. You can find the article here: Texture Resolution Tips