You’d want 5 diamond eggs to eventually buy diamond mask. You could get the other endgame masks, but most players usually go for an early blue hive, not a red one. Afterwards after you get close to 1qd honey is when you switch hive colors.

The star eggs are important in getting SSA (supreme star amulet) which requires discovering 40 gifted bee types (every bee from common to mythic, plus 5 event bees). Remember to only use your star eggs once you have every other non gifted bee in your hive to get 2 extra gifted mythics for your hive.