You have to do one at a time. How much fat you gain with the muscle depends on the quality of your diet, but you have to eat extra food. You simply cannot gain weight or muscle without eating at a caloric surplus. It's biologically impossible. Calories in have to be higher than calories out. At 168 pounds, you're not running the risk of getting fat any time soon, so I would say you should bulk.

From the sounds of it, you're probably "skinny fat" like I was. That is, tall and skinny, but have a bit of a tummy and not very muscular at all. My inclination was to try and lose my gut by cardio and dieting. I spent two years trying to do this. This does not work. You just get skinnier and skinnier and the gut never goes away. You have to add muscle first. Then once you have the foundation of lean body mass, then you can get rid of the gut. This took me a solid 2-3 years to figure out. Don't make the same mistake. Suck it up and take the extra 4-5 pounds of fat for the six months. It'll be worth it in the long run.

But when you bulk, don't eat like an idiot either. When I first bulked, I thought, "Hey, I need to eat 4000 calories, I'm going to go buy a bunch of cheeseburgers!" Don't do that. You'll add more fat than muscle. And once again, I wasted an entire year. Now that I finally got this shit down I'm REALLY kicking myself for wasting so much time and effort in the gym when my diet wasn't in check. Working out aimlessly won't get you anywhere. Or worse, it'll get you the wrong results.

It's totally counter-intuitive, but the skinny-guy-gut doesn't come from excess fat, it comes from lack of muscle. When you add 10-15 lbs of muscle to your frame, your shoulders broaden, your chest gets big, your back gets big, and suddenly that little pooch looks tiny in comparison. Eat big. Eat clean. Get the muscle first. Then trim up.