Ryan,
6'1 122 lbs is very skinny. However, you have an excellent frame to build upon. 6'1 at 16 years old is a good height and I think you will probably top out at 6'2 - 6'2 1/2 depending on your genetics.
I completely understand the idea that you do not want to eat crap, and frankly I agree. I would eat a gigantic amount of carbohydrates and protein mixed in with a moderate amount of fat. At your age your metabolism is like a furnace and you will have to eat like a horse to gain weight.
However, I would caution you about eating everything in sight. I did that when I was 16. When I was 16, I was 6'3 170 lbs. Yuck. I gained weight and reached about 205 lbs in a year by eating everything in sight, but I became pretty fat in my midsection. Sloppy fat. My body was very soft and not muscular. I hated it. I went from having abs to having slop. I found myself regretting most of the weight I added, and just went backwards trying to lose the slop that was covering my abs. Sometimes its better to just gradually add weight at a consistent and steady pace. It will take longer to gain weight but the weight you gain will be quality mass and in the end you will be happy that you chose this path (at least if your goals are similar to mine, which is to have low bodyfat!).
I would eat at least 4,000 calories a day, perhaps more. 800 g of complex and simple carbs (3200 calories), 100 g of fats (Flax Seed Oil and Fish Oil are key! they slow everything down and help you add more weight) (900 calories), 300 g protein (1200 calories). Thats roughly 4000 calories. If you are not gaining any weight at 4,000 calories a day you should definitely increase calorie intake. Monitor your weight every day. just be aware though that your body fluctuates 5 lbs a day: meaning, I usually wake up about 5 lbs lighter than I went to bed because of the water weight I pissed out and the fact that my glycogen deposits are somewhat used. So just keep that in mind if you weigh in when you wake up.
Everybody has a different way of achieving a goal. Like the other helpful EF bros said earlier, some people choose to eat a lot of fat while others like to keep it clean. Choose the way that you feel most comfortable with and go with it.
If you need anything else, EF is definitely the place!