Lets say I have made survey using a sample of a given number of people, containing a set of 25 questions that have 6 possible answers (Fully agree/ Partially Agree/ Neutral/ Partially Disagree/ Fully disagree/ Don't know), and a few other questions concerning variables I'll be using to qualify them (such as gender, average income, region of residence, age, color, and so on).
Now lets say I want to try and find correlations between gender/race/age/etc and the specific answers given to the set of the 25 questions. Lets say I also want to see if there might be correlations between answers. In other words, I want to find all possible correlations among these variables and the questions, and among the questions themselves.
Should I be thinking about using a Multiple Correspondence Analysis for this objective, or a Multinomial Logistic Regression, or maybe both, or some other specific technique?
I've been studying statistics by myself and I'm confronted with this problem and unsure of what path to follow. Both ways seem to want to find similar answers, but there seem to be nuances in choosing which one to use that I am missing.