So, I want to do some martial arts, for self defense. Ideally one that will be useful without giving me CTE, or any long term bad stuff, even though I feel this is already asking for too much 
I don't live in the U๐๐ so gun related stuff isn't really an option.
I'm somewhat heavy, with a year of experience in lifting, and my cardio is not the best, but I can do long walks (of 1 or 2 hours) before getting tired.
I'm going to move to a bigger city in September, and there's a lot of stuff available, so you can comment on the more niche options.
So yeah, any advice from your experiences is welcome lol
If I had known people started arguing over my post I wouldn't have made it.
Just because cops are saying it doesn't mean it's not true. There's actual studies on the matter and they've done testing. Drawing a firearm and shooting accurately enough times to consistently disable a human immediately - so at least two shots with handgun calibers - is extremely difficult and cannot be done consistently within that range or closer, and again most self defense starts within or just outside arms reach.
That's a large part of why they themselves teach police basic grappling. Most of them aren't any good at it, but they are still taught it for good reason.
Again, it's a matter of consistency - if you try to draw a firearm when someone has hands on you, they are GOING to attempt to stop or disarm you by grappling you, even if likely in a clumsy untrained way.
Obviously, it's much easier to resist grappling when you yourself know how to grapple. It's a skill, after all.