3 cards in deck are downloaded during the seed phase:
Takket and Taurus (by Assign Mission Specialists)
Always a Chess Game (by Continuing Mission)
Q's Tent cards are downloaded by cards during the play phases of the game:
D'deridex is downloaded by Attention All Hands, usually as your first turn's card play.
The Art of Diplomacy is downloaded by Neral, as soon as he hits the table. It can then be discarded to download Romulan Disruptor.
Captain's LogORDefiant Dedication PlaqueORLower Decks can be downloaded by Tomalak. The Log helps with ship battle, Plaque helps you get places faster, Lower Decks helps with mission solving. Your two matching commander pairs are Tomalak/Derenas and Mirok/Apnex.
ApnexANDEstablish Landing Protocols are fetched by Hidden Fighter. There is no reason not to get them both.
Space Boomer is downloaded by Agyer; it only boosts range once you've solved a space mission.
Espionage: Romulan on FederationORStrange New WorldsORHinder Progress are downloaded by Admiral Mendak. The espionage can be used to attempt Earth if the opponent seeds it. The other ones are very situational hindrances.
Romulan "Reunification" comes from Sela, but only if your opponent seeded Vulcan (you don't have it). Almost never relevant.
Dilemma Pile Strategy
D: Distracted -> Spatial -> Chula
D: Incentive-> Berserk -> Unscientific -> Scientific
P: Rules -> Denevan -> Friendly -> In the Pale
P: Lack -> Jol -> Hippocratic -> Medical
S: Your -> The Ghost -> The Arsenal -> Gomtuu
S: Edo -> Female's -> Up Yer -> Cytherians