My guess is you need the Neural helmet on Fighters and Bombers, if only for the perspective Imaging.
When you start getting into Transport class and above you don't need them because there's enough room on the bridge for holographic displays and such. And on the Flight Suits... Depends on the ship. Something like the Avenger or Titan, they might be optional, but ships like the Jackal and Bulldog would need Both Flight Suit and Helmet due to the unstable nature of those ships, don't want to risk "I... can't... Breeeathe!" (I love the Raspy Pirate VA's ham factor his lines)
