Of course, there's no way to be sure what a person will or won't like, but I can say that I'm a fan of all the shows you listed under likes and I dislike everything you listed under the other column, and I love Firefly. In response to your question, there are absolutely no aliens on this show. Its really mostly about a bunch of Average Joes in space and the humor comes from normal banter between friends and rivals. I'm the same way you are with Buffy: I just didn't get into it. I can definitely see how there's a similarity in the writing style in that there's humor thrown into the action, but in this case it just fits with the characters. Rather than questions about anime or Buffy, perhaps the best question is: Do you like Han Solo and the Millennium Falcon? That is, after all, the main inspiration for the show.
Also, if you're planning to start on the series, you may want to begin with the episode Out of Gas. Due to some issues with the network, there were actually two pilots, neither one of which is that episode, but this one is the episode that establishes how the crew was put together. Its your call, though. Another way to start could possibly be with the film Serenity, since its probably easier to come by. On the other hand, its definitely the last chapter of the story, so I recommend just starting with the series if you're looking to really enjoy it.