choosing basic test: logistic regression or multiple chi square?



I'm new to statistics and am working on a project for work. I have read extensively and believe I am on the correct path, but would like to check and make sure:

I have one dependant variable of outcome: had reaction or did not (nominal)

I have multiple independent variables, some nominal (have disease Y/N), some ordinal (number of medications) and some measured (age).

I was planning on converting the measured to ordinal based on groups and then running a logistic regression on the analysis to determine which factors influenced the final outcome.

an alternative approach would be to run multiple chi square 2x2 (or I guess that would be fisher, depending on sample size) on each variable. I thought tthis would take a long, long time.

Am I starting on the right path? Is there a better test to get started with?

Thank you for any starting tips and advice. Also, if there are any good reading references, I would appreciate it as well. I'm not just looking for an answer, but to learn.

Thank you.