First of all, what kind of fighting are we talking about here? If you're worried about being attacked on the street, the best advice is simply to pay attention to your surroundings, not go into bad areas where things like that happen more often, etc. If you do that, chances of being attacked etc. are pretty low.
When it comes to true self defense, unarmed fighting should be a pretty low priority. I suggest applying for a concealed weapons permit, purchasing a firearm, and getting training in how to use it. Real life isn't like the UFC, there isn't going to be a referee there to make sure everyone fights fair, and there's no reason not to use the best tool available for the job.
BJJ is great, but outside of BJJ gyms, people throw punches and gang up on other people. You need to learn how to hit and be hit, and training one vs. one without strikes while learning how to choke someone with the collar of something they'll never be wearing outside of a BJJ gym isn't going to help with that.
If weapons aren't an option, learn how to box and combine that with some basic wrestling or BJJ (no gi only), with emphasis on takedown defense. You don't need to learn how to do the spider guard and escape from arm bars and stuff like that if you're just learning to defend yourself on the street.
Lifting weights is great, but it's pretty low on the priority list when it comes to self defense. I've never seen a barbell throw a punch or pull a knife on someone.