Starter ships are the first ones you manufacture, so they are low-tech small and cheap ships.
For those, you typically want shuttles or small corvettes that take up the least amount of materials and time to build. Usually the type is "Spaceship", and they lack high tech like transporters, shields and FTL drives.

Early shuttles, no gravity & FTL techs (no eludium & lumenite) :

• AEC Draco Dropship (Rocket)
  
• Atlas Colony Ship
  
• LP Rocket Speeder
  
• UT-47 "Rocket"
  
• Rocket
  
• Tethys Light Shuttle - Rocket

Classic shuttle, gravity tech but no FTL techs (using eludium but not lumenite) :

• UAZ-3306 "Space Bukhunka"
  
• AEC Draco Dropship (Mining)
  
• LP LowTech Worker
  
• Explorer II (requires vulcanite)
  
• [UNSC] D77H Pelican Beginner
  
• Small Ghomship
  
• AEC Draco Dropship (Beam)
  
• UT-47 "Kodiak"

Those ships usually are bulkier than shuttles, because they need to house a beam gun and long-range sensors. They often don't get unnecessary techs that could ramp up the cost or diversity of resources required, since the Asteroid threat is both urgent and a one-time issue. They often are using gravity techs, beam weapon bays and sensors.

Dedicated asteroid hunting ships :

• Ibis "Busteroid" Corvette
  
• AEC Draco Dropship (Beam)

Those ships usually are small, produced on ground and use wormhole FTL drives. Some may require advanced techs like shields and transporter.

Early FTL shuttle, using lumenite but no eludium (FTL tech but no gravity tech) :

• ESI Finch WHD
  
• Rocket FTL

Classic wormhole FTL ships, using lumenite & eludium (gravity drives, WH FTL, no advanced techs) :

• AEC Draco Dropship (PNN)
  
• LP LowTech Nomad
  
• AEC DRACO RETROFIT
  
• AEC Draco Dropship (PNN+Tur)
  
• Pig Transport
  
• Turbo
  
• Scout
  
• Basic Design
  
• Basic Design Ballistic Turret

Wormhole FTL ships using advanced techs (gravity drives, WH FTL, shields, transporter, no WARP) :

• Firefly One rev-c (using transporter)
  
• Ibis Corvette (using shields and transporter)

Stations are stationary spacecraft that act as both an orbital trade hub and advanced shipyard, in addition to be able to defend a city if it has weapons. Rocket-drive stations are not mandatory, they are here only in case you really need one before having access to eludium.

Rocket-drive stations (no eludium, no gravity techs) :

• Del Rey Station - Rocket

Standard gravity tech stations (no advanced techs) :

• Inflatable station
  
• Del Rey Station - GDrive
  
• LP LowTech Station

High-tech gravity stations :

• LP HighTech Station (using transporter tech)