Jessica Mason will become a playable Specialist.
I don't see much other reason they'd be setting her up as much as they are, given the lack of a traditional campaign.Jessica will be revealed as having the callsign Spectre.
Classic Price is an Archetype of the rebooted incarnation of Captain Price.
Despite the fact that the version of Price that was made playable for those who pre-ordered the reboot is clearly based on the original incarnation of Price, due to the canonical links established between the reboot and Call of Duty: Black Ops Cold War, it's possible Classic Price is canonically an Archetype similar to the other classic characters playable in Blackout. A clone of the rebooted Price, rather than one of the classic character.