How to convert an HTML website with stylesheets to Drupal 7 nodes?
What you are looking for to avoid creating a whole theme from scratch is known as a starter theme.  Starter themes are special themes designed to not work as themes by themselves, only to be used as foundations for a theme you build on top of them (the latter is known in Drupal-speak as a sub-theme). I.e. starter themes are theme framworks that "reset" the CSS, so that you can rebuild the CSS without having to think about inherited styling.

Pick the starter theme that looks like it best suites your needs, and build on that.

As for stater themes: Zen is the one that most people use. The other one I will recommend is Basic.  It is a stripped down fork of Zen. As a bonus, both are responsive by default.