Your core isn't big, it is that it is normal size and the rest of you is small. For getting bigger while having it transfer well to MMA, I'd say just do strength work, then include some higher rep stuff for your back, pecs, shoulders, etc with controlled eccentric and all of that other weird bodybuilder stuff.
For programs, maybe try westside for skinny bastards, cube, or westside (in order of how hard it is to fuck the program up starting with hardest to easiest left to right). I've tried two out of those three, and I've trained similar to the third before, they all work well, and are sound programs.
One last thing I need to stress, you need to gain weight. Don't go add 30 pounds immediately or whatever ridiculous number you can think of, but do it gradually, you want to gain about 2-3 pounds gained per month, and do that for about a year. After about a year, try losing weight at a nice and steady pace (about a pound per week is good) until you are about as lean as you are now, then repeat the process. You should net a good amount of muscle each time.
It will take awhile to get where you want to be, and it depends on how consistent you are, how dialed in your training and nutrition is, and if you do it assisted or not assisted. You definitely don't have to be assisted to do it, and I don't recommend it for legal and health reasons, but it does do amazing things if your training and nutrition is dialed in.