Which Statistical Test to Use?

#1
I am doing a research project in which I have collected variables on two separate groups. One group uses a self testing laboratory machine which I have labeled as "patient self testers" (PST). The other group does not use the self testing machine, "non-patient self testers" (non-PST). The intent of my project was determine characteristics of the PST group that make them "good" or appropriate candidates for this self testing machine (e.g. age, diabetes, etc). Once I have collected all the information, my intent was to apply these "good" characteristics to the non-PST group in hopes of converting them to PST. The variables I collected on these groups include mostly nominal/ordinal data with the exception of age and distance from clinic.

I am struggling on which statistical test would be appropriate now that I have collected all of my data.

I think the most appropriate test is a correlation or regression, however I not sure on how to do this with mostly nominal data. Also am I able to run multiple different tests for each characteristic (about 11 total) without confounders?

I would really appreciate some guidance in the right direction.