First Class is broken down into: First Class Letters and Postcards, First Class Flats, and First Class Parcels.
More info here:
http://pe.usps.com/RateCase2007/DMM300_HTML/ratesandfees2.htm
You'll see that "First Class" appears under the "Letters", "Flats" and "Parcels" category. you just need to figure out which of the 3 your package falls into. (probably not "Letters"!)