Correlation testing of survey results

Hi there, hopefully this is posted in the right section. If not, I apologise.

I have been helping out a local charity to compile and analyse a service user satisfaction survey and would like to perform some equality testing (age, gender, ethnic background and sexuality) against the results to check whether the organisation is performing adequately for different groups.

I have some experience of doing some correlation testing (Spearmans and Pearsons) but it was about 20 years ago and I'm unsure which to use or if they are even applicable to the data we've collected as I can only really remember doing it with quantitative data, but think what I've got here is qualitative data.

So, the results for the equality testing are broken down thusly:
Age: 16-24, 25-34,35-44,45-60,over 60
Gender: Male, Female
Sexuality: Hetrosexual, Gay/Lesbian/Bisexual
Ethnic background: White, Mixed race, Asian, Black/African/Caribbean

And an example of the choices available as a response for one of the questions are as follows:
Excellent, Very good, Good, Average, Poor, Very poor

I'm only looking at testing one variable at a time, eg clients age group, as opposed to testing age group and gender.

So what test do I need to perform, and if possible, could you point me to an example that directly applies to the form of data I have.

Many thanks in advance,
The Cageybee