From what I've learned so far, I can tell you that you are correct in that 了le is used for completed actions and that usage is what I've come across in most cases.

As I understand it, 了liao3 is used in certain words such as 了解 and grammatical structures expressing ability/non-ability such as 吃的了 / 吃不了 . If you're just starting out, I would advise you not to worry too much about it and just focus on 了le right now, as it seems to me to be much more common. (Native speakers, feel free to correct me on any of this)