USPS uses weight to determine shipping costs and your product weights were set to zero, so no shipping rate could be calculated. I added code to only allow free shipping for orders over $100. That isn't normally an option, so I had to hand code the update in the shipping plugin.
First Class shipping is only available for certain items. You can send standard postcards, letters and large envelopes and small packages up to 15.99 ounces using First Class Mail. If your First Class package is over 15.99 ounces, you must upgrade the mail class to Priority Mail. If the purchase is over weight then it will not show the first class option.