I must create Wordpress sidebar widget such as this one:

As you can tell its fully graphic and that i would like it to keep style no matter Wordpress theme installed.

How do i do this within Wordpress ?

I am talking about to get rid of H tags or any other needless tags with this particular widget ?

Start here: http://justintadlock.com/archives/2009/05/26/the-complete-guide-to-creating-widgets-in-wordpress-28

Next: http://divitodesign.com/css/style-wordpress-widgets-with-css/

So as the possess the widget's style be theme neutral, you will need to set or load the css inside the widget function, so that your specific selectors and graphics could be globally applied.