By default priority mail is not enabled for carrier calculated (because GCO used to have problem). However, it's working fine now so you can turn it on in the file (not admin side) if you want to offer priority mail. Carrier calculated also doesn't support First Class Mail.
Keep in mind that the fixed/variable fees is not calculated right either by GCO when using carrier calculated.
Unless you really have to, you might want to consider using merchant calculated shipping.
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