Gobies are cool but many do have a tendency to dig, which can upset rockwork and cover your corals with sand. I think that part about them "protecting the cleanup crew" refers to the fact that some will pair up with a certain kind of shrimp, sharing the hole.
Corals can be aggressive, sending out tentacles to sting and sometimes even digest other corals. Again, research is key. You will have to learn just how closely you can pack in different types of corals.
Soft corals are the easiest to keep in general. They do grow quickly so keep that in mind. LPS (large polyp stony) corals are usually second. Acanthastrea is supposed to be one of the hardier LPS members and often very cool in terms of colors.

I would suggest looking around and noting the corals you like the look of, then researching thoroughly to decide if they are right for you and your tank.
An anemone (nem for short) could be done, but not right away and preferably not in a tank that size. To be honest, I personally would not go with a tank that small. I have my first reef attempt in a 20g, and given the choice I would not do it again. It's too hard to keep the parameters stable in that water volume. This is a problem when keeping an anemone, as they are quite sensitive to such things. If it were me, I would wait until I could upgrade my tank size.
Edit: That reminds me...a lot of stores will suggest a sixline wrasse for a tank that size. Don't fall for it. Some are peaceful but more often they turn nasty enough to kill your other fish, even fish bigger than they are.