Zoas are a great beginner coral, but do be careful about buying corals (or any other livestock) that you haven't researched before hand. At the very least bookmark LiveAquaria.com on your phone so that you can do a quick read up on whatever you want to buy before making a big mistake and wasting money or killing a critter.
Nope, that algae growth is really common in new tanks. But I wouldnt let it get out of hand, keep up on the water changes, dont over feed and dont overstock.