Running is not going to get your legs in good shape. Just because your family runs does not mean you can ignore your legs and lower body.
You should ditch this program and get on a good premade one like a Pavel 3-5, Starting Strength, 5/3/1, etc.. Also start going to a real gym that has the proper equipment and stop limiting yourself by the poor selection offered by the place you are now.
A ketogenic diet (like the low carb diet you are describing) is not ideal if you want to build any sort of muscle. In the long run, it will cause you to lose muscle and will deplete your energy in the gym. If you are going to be doing intensive exercise, look into carb cycling. Also, I would not bother with the supplements besides the fish oil and creatine. All you need for a post-workout shake is some whey protein and carbohydrates (dextrose and maltodextrin are good choices) mixed in water.