Most of what people like about Firefly is the character focus, not the story per se. There's some of that, certainly, and what there is certainly entertains; but it never really had time to go anywhere story-wise.
It did push the characters hard, though. You may not notice it now, but on second viewing you'll be surprised at just how much depth some of the early episodes have in that regard.
There's a sentiment I've heard quite a bit regarding the show: That we'd watch these people eating dinner for a hour, because they're just that fun to hang out with.
The next big push on the River story is in "Ariel".