Is the term "Everything happens for a reason" appropriate? In terms of  Buddhist thought Is this accurate? It doesn't seem to jive with cause and effect which is more often referenced.
The issue concerns the way you understand the statement "Everything happens for a reason", since 'reason' has various meanings.

'Reason' could mean motivation or intent. For instance, "Someone has his reasons to behave the way he does." If you have that meaning in mind when you read "Everything happens for a reason", you will think it means "Everything that happens was intended by someone, like a creator God." Of course, this would not be Buddhist.

'Reason' could also refer to a cause, as in "The reason for his absence is sickness." Then, "Everything happens for a reason" means "Everything that happens has causes and conditions." This is a correct statement, from a Buddhist viewpoint.

I would not be surprised if 'reason' could also mean 'purpose, aim, goal' but I can not find an example.

We do not hear "Everything happens for a reason" often in Buddhism. I myself would never even think of saying it, because it is vague. In addition, I feel that most people would misunderstand and think that it means "things were intended this way" or "things will eventually fit in a big meaningful picture."

A more common way of stating things is: "You created the causes of your suffering." This is more personal and it is aimed at taking one's responsibility.