I'm 5'11'', 180lbs and my fancy new scale says i'm ~22% bodyfat. I carry almost all of it in my stomach.
I've been at the gym 3-4 times a week ~10 minutes on the treadmill around 7MPH
then the best workout I can do at the gym in my building (no barbells, just DBs & machines): 12,8,5 Pull Downs 12,8,5 Chest Press 12,8,5 Tricep Extensions 12,8,5 Cable Curl 12,8,5 Incline DB flys 12,8,5 DB Press 12,8,5 Lat Raises
I've been very low carb since I started this 2 weeks ago (<20g a day, except carb up days ~100g). Consuming ~200g protien a day. Creatine, Fish oil, finished 2 weeks with a fat burner (about to switch to HOT-ROX) just started phosphatidyl-serine. My workout drink is scivation xtend.
I've always been a "skinny" guy, but I developed a gut over the past few years. My goal short & long term is to transform my body into something I'm not embarrassed about a day club pool type place.
ditch that crappy weight circuit - the best you can do there is DB swings, 1 leg deadlifts Goblet squats, 1 leg squats, lunges 1 hand DB overhead press, DB bench DB rows, DB cleans and Snatches Bodyweight stuff - google beastskills
I find that a dumbbell deadlift is a completely new challenge compared to a barbell deadlift. Pulling 180 lbs off the floor is a lot easier for me than pulling two 90s off the floor. Consider that.
Track your waist, chest, and weight once a week after using the bathroom, before eating/drinking anything. When I do it it reassures me that I'm on the right track even while I don't notice changes in the mirror immediately.
I know most people are giving suggestions for getting around the lack of equipment, but in all honesty I would find a better gym. This might be hard on you financially, if this is the issue, but it will pay off in the end.
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.