Some things you might like to know before going into watching the series:
1. The pilot episode is also called "Serenity".
2. Much like Star Trek TOS, Firefly was aired out of show order. The episode they used for the pilot was called "The Train Job", and is considered one of the weaker eps of the show...although I personally loved it.
3. I think only 12 of the 14 eps actually aired, with Serenity ( the pilot) being among the two that weren't.
4. If the lovely Jewel Staite (Kaylee, the ship's engineer) seems a little bit heavier in the series than she did in the movie, that's because she was apparently asked to put on another 10-15 pounds for the character, to make her cute, but slightly frumpy.