Just thought I'd butt in on this topic...I have a part time job running the post office at a dorm on my college campus.
First Class mail usually takes 2-3 days to arrive, depending on distance. Priority is the same thing as First Class mail, exept it was designed for parcels heavier than 13 oz and has a fancy name. It also usually takes 2-3 days to arrive. A lot of people think that Priority is faster and more reliable than first class mail, but it's not true.
I haven't heard of a Post Office ever giving a refund because a Priority or First Class parcel is delivered late. USPS makes no guarantees on delivery dates, and there isn't any kind of extra service you can buy (delivery confirmation, certified, etc) that will make it arrive by a certain date. The only form of USPS mail that is guaranteed to arrive by a certain date is Express Mail (and yes, you can get a refund if it does not arrive on time).