gobies can jump, check behind your tank and in the overflow. he could just be hiding.
anthias are very difficult to keep, not recommended for a beginner. they really take a lot of care. you have to entice them to eat, and most people suggest feeding them 2-5 times per day, which can be difficult if you have a job. they need to constantly eat, especially when young.
once they hardy up, they certainly can be fed less and in larger portions, many do this with success, but this is after 6 months - 1 year of intense regimented feeding. i'd recommend against them. plus, you really could only have 1 in your tank, and the tend to do better in schools.