You should try to improve your lighting first. It is not equal on all parts of your document, so the upper left corner is much darker than the lower right corner. It means you will have to use gradients when post-processing. You can do that, using PS, Gimp or IM, but if your input is better, the better your output. Also, your pictures have lots of noise, probably because you are using a high ISO level on your camera, usually very bad on compact cameras. If you improve the lighting you will be able to use a lower ISO level, like 100 or 200, giving you more details and less noise
To remove the background, you usually play with the levels, setting the white and black points to reinforce the blacks and change the greys to white.
There are tons of methods to do this, using level adjustment (http://nyfalls.com/article-photoshop-levels.html
), contrast-stretch, layering (see for example http://www.imagemagick.org/Usage/compose/#divide