If you want to defend yourself, you really ought to know a bit of both (striking and grappling), because somebody could always grab you when you don't want them to, and you might want to get away from them... and somebody could always take a swing at you, and you might not want to get hit by that punch.
I'd say you want to pick at least one out of this group:
-boxing
-muay thai
-certain kinds of karate (many are impractical)
(NOT most Chinese martial arts or tae kwon do, at least as they're taught in America these days, unfortunately. If they're not ever sparring, they're teaching you make-believe.)
and at least one out of this group:
-wrestling
-judo
-bjj
Or you could go to a good mma school. Back in the early 90's somebody famously said, "If all the different martial arts fought each other and there were no rules, who would win?" Twenty years later, it turns out the answer is: somebody who knows grappling and striking--otherwise it's always possible to get caught up in a situation you can't do anything about. There are some Korean martial arts that teach both striking and grappling, too. And, honestly Krav Maga is probably a good option for a lot of people. If you're not really that interested in martial arts, and you want some good self-defense basics in a reasonably short amount of time, Krav Maga does that pretty well. That's mostly what it was designed for.
Unfortunately, it's can be hard to tell whether an mma school is a "good" mma school, or whether it teaches effective self-defense before you go there for a while. Martial arts is kind of always a journey.
Martial arts should be fun, and a good workout. It can also give you a little bit of an idea about how to keep yourself from getting hurt by another person, which can be pretty empowering. That said, the world is pretty chaotic and there are some situations martial arts aren't going to help, and there are no guarantees.
As to the question about size/strength in striking and grappling:
In my experience, between two relatively skilled hobbyist strikers or grapplers, size/strength matters less in striking. I've outstruck a lot of guys that I could never outgrapple, because they were too much larger to deal with once they get a hold of me.
Maybe more pertinent to your question, if you do a year of hardcore bjj, going to class a few times a week and maybe drilling a few things on your own at home--you should tool an average guy on the street after that. On the other hand, if you have never done a striking art before, and you do a year of boxing, you'll probably still tool an average guy on the street, but I think it's less certain. I think it takes a little longer to get that head movement and balance, and really fast, easy, loose hands that would let you just clown somebody.
If you do boxing for a few years, though, somebody could be swinging at you, and you could make them hit nothing but air, and then knock them silly pretty easily. It looks really cool, too. I love doing that. Whereas with grappling you have to get all up on them, and you get dirty and undignified, and half the time in the street random other people will jump in and do things to two people on the ground.
