Anything above fighters, and probes can claim planets. If you get either Tier 1 Combat - Offensive Initiative, or Tier 1 Trade - Remote Harvesting, they will allow you to build ships needed for claiming planets.
I noticed a bug in the invite code just before the release. Rather than delay the release yesterday, it was disabled till we could look at it to see what the issue is. Should be corrected shortly and back in the game.