ksteliou,
In my experience, more important than the particular coral is your lighting and water parameters. While phosphates levels arnt that big of a problem with fish, corals can be much more sensitive to them. I have been using a ferric oxide media (the small, rust colored pellets) for quite some time with great success in removing phosphates.
Nitrates are usually best keeped as low as possible, with 40 ppm and under being good for most.
With Calcium and Alkalinity, a high calcium level is going to speed growth, but the Alkalinity is going to stabilize the pH level, which is much more critical to coral health (fish health too for that matter).
Getting back to your question, I group corals in three very broad, general categories- Leathers, Large Polyp Stonies and small polyp stonies. The first two tending to be better beginner corals than the third group. My favorites to start out with are the sarcophyton (toadstool coral) and brain corals of various kinds ( favia and platygira are both pritty cool). Leather corals can also be very cool, adding movement to the tank. Green Nepthias and "Devil hand" coral are two that I like.
The corals above would do well under "moderate" lighting, as in a good fluorescent fixture.
I hope you find this information useful and best of luck
-Paul