So, it seems we will mostly see Federation and Klingon ships. What would be some good existing clix dials to use with them for other ships?

Something with Stealth and Flight for Romulans
Sentinels for Borg

Also some other ships from other series

Star Wars
BSG
B5
WH40K Battlefleet Gothic

Any others you might think of?

The Sentinels are a really good call for the Borg.

Sentinel Mark V (GSX G02)

WE ARE THE BORG (Running Shot)

Force Blast

ADAPT AND ASSIMILATE: Sentinel Mark V can use Outwit. Sentinel Mark V can use it normally, or Sentinel Mark V can use it targeting each opposing character with two action tokens that is within 10 squares and line of fire. You may counter a different power on each character.

RESISTANCE IS FUTILE (Charge)

OVERWHELMING SIZE (Flurry)

DRONE BOARDING PARTIES: Sentinel Mark V can use Incapacitate. When it does and hits, choose one: a hit character can't be moved by any game effect until your next turn; or a hit character receives two action tokens.

ADAPT TO SHIELD FREQUENCY (Penetrating/Psychic Blast)

ASSIMILATE RESOURCES (Super Strength)

REDUNDANT SYSTEMS (Invulnerability)

ADAPT TO YOUR WEAPONS (Toughness)

DISPERSAL FIELD (Energy Shield/Deflection)

SELF-REPAIRING (Regeneration)

Ranged Combat Expert

HIVE MIND (Enhancement)

INCORRECT STRATEGY, NUMBER ONE (Close Combat Expert)

CUTTING BEAM (Exploit Weakness)

Not to mention the "Assimilation" of capturing ships with the older Sentinels.