One of the least expensive fish you'll add to your tank will be the blue & green Chromis fish. They are in the damsel family, and in a large group will shoal together all day long. Their silvery bodies nearly glow under reef aquarium lighting, and their activity will make your reef come alive. Chromis will eat most any food added to the tank. They prefer to tuck into various corals for protection at night, and their favorite colony appears to be the Birdsnest coral.
Over time, their numbers will dwindle in your aquarium, seemingly survival of the fittest. If you like, replenish their numbers from time to time. I would recommend quarantining new fish as they may bring disesase with, so err on the side of caution by using a quarantine tank.
If you happen to spot these eggs in your tank, they are very likely Chromis eggs.