I have been following a lot of "anime you should be watching" lists online, mostly from sites like kotaku. There are a few places you can watch legit anime online like Crunchyroll or Hulu, the just add commercials but those can be blocked with addblock plus.
The Five Best Anime of 2013
Some anime I have been watching recently:
gargantia on the verdurous planet
the devil is a part timer
school days
Attack on Titan
And Im about to start Gatchaman Crowds.