Fair warning: Fallen Spire significantly changes the game, if you decide to pursue its storyline. Depending on the difficulty levels you play at and the degree to which you build chokepoint fortress worlds, you may also find that your game strategy needs significant adjustment if you decide to pursue a Fallen Spire campaign.
I'd also rate Riot and Protector Starships as more fleet-support, while Spire Corvettes and Champions would tend more towards fleet-damage, just in case that matters to you (incidentally, Fallen Spire customizable ships tend more towards fleet=Fallen Spire ships).
(Just in case you don't have it, you need the Light of the Spire expansion or its demo in order to start a game with the Fallen Spire option enabled, and the demo most likely won't allow you enough time to play enough of the Fallen Spire campaign to get into the ship design parts of it. The Ancient Shadows expansion and its demo, with the up to eight champions you can play with and the Spire Corvette bonus starship, offers more immediate ship design options which are available from the start of the game. Protector Starships require the Vengeance of the Machine expansion or its demo, and like champions or Spire Corvettes can be available from game start.)