Go with the basics to begin with, find a dojo (martial arts school) that includes training in street defense, not competitive tai-kwan-do or the likes.
As for ju-jitsu or krav maga or any of the other fighting arts (the Asian arts usually do not end in -do, like ia-do (Japanese fencing) , but itsu like iatsu (real swords, real fighting, kind of), these are usually full contact training - not a bad idea, part of the skillset that Gabe Suarez uses in his force-on-force firearms training using training rounds instead of Airsoft or the like. If you're middle aged, it may be more than you can handle. From what I have seen, you will get hurt, and that is just in training!
IMO - go with a dojo that offers self-defense, often coupled with women's defense training, especially if they will do 1-on-1 training or a small group (2-4) instead of a classroom full of people.
My $.02.
Look at aikido too. O-Sensei in the 1920's successfully defended himself for 8 hours against a Japanese Naval officer with a sword - the real kind. O-Sensei never armed himself, but wore the other guy out.