I am going to make a new responsive theme based on an existing base theme for drupal 6. The theme need to be minimal but flexible. As there are many CSS grid systems to choose from, I've read that 960.gs has fallen out of fashion as it is too small for current monitors. So I'm wondering whether there are any important differences between fluid and non-fluid ones, and currently what are the best options available and why?
Ok, there is no single best answer. It really depends on your needs.
In my opinion, the difference between fixed with and fluid grid has more to do with the theme you want (and your art director). Not all designs will work with fluid grids, especially ones that require pixel perfection.
That said, there are techniques that you can use to have a fixed grid, but have it adaptable for different screens. Basically, you design a few grids with the link above, and then use CSS3 Media Queries to load the grid you want based on screen size. This is precisely what the Omega Theme does. I have good results with this approach (though with the Drupal 7 version), and highly recommend it rather than tacking on the grid to another base theme. I used Zen 960 a few years ago, and ended up fighting some of the automatic grid reassignments that it did.
If you go with Omega, just note that the grid-24 that it includes is slightly different than the one from 960.gs. This means that you can't use the 960.gs templates with Omega's grid-24. You can
hook_css_alter in the sheets from 960.gs without any side effects (Drupal 7), or use other shenanigans for Drupal 6 to change the sheets you need.
If you really do need to retrofit an existing Drupal 6 theme (and can't use Omega), then I think I would sledgehammer in the multiple-grid approach that Omega uses directly into page.tpl.php.