Luckily, I came across the small Brief Firefox extension which fulfilled all of my wishes. It’s lightweight, it’s a firefox extension, and it has the “unread”-folder as well as a nice and elaborate handling. It’s content-view is skinnable (though I have yet to come across a skin that suited me better than the original one), there are a handful of reasonable options, and it integrates with the Firefox-RSS-capabilities as well using it’s dynamic bookmarks system.
It’s just as the synopsis on the homepage says: “Brief is a light-weight feed reading extension for Firefox. Designed to be easy to use and streamlined, with exactly the right set of features.” – ’nuff said.

So if you happen to be in the market for RSS-Readers, make sure to check this one out.