I'm new to data analysis and I've been messing it up by using Pearson's correlation coefficient to measure possible relationships between different variables in my data set, both dependent and dependent, discrete and continuous.
Today, I read that using Pearson's on categorical data is a no-no unless there are only two categories, and that those categories must be 0 or 1.
Then I read that using the correlation ratio $\eta$ is good for categorical variables with greater than 2 classes.
Then, I read that I have to consider whether the variable is nominal or ordinal before I choose how to measure relatedness.
What are the best practices for assigning a measure of relatedness to the following types of relationships?
A little bit of theory is welcome as I'm not a stats guy and I'm always interested in diving below the surface. However, I'm mostly looking for a concise answer that allows me to move forward in my analysis.