When I started seriously lifting (about your age, I'm 19 now) I started by learning as much about the human body as I possibly could, regarding nutrition, what muscles perform what actions, so on and so forth.
Some basic rules I came along with is to cycle in different exercises for each body part (depending on your split), try to not spend over an hour in the gym, time your rest intervals, make sure your form is immaculate, make sure you always do warm up sets, and most importantly EAT BREAKFAST. These are pretty basic rules any serious lifter will tell you to follow.
As far as training goes, there are immense amounts of great articles on training splits on this site--take time to look over as many as you can, and the philosophy behind them. Try ones that interest you for at least 2 months before deciding whether or not its something thats for you. Pay attention to the signs your body gives you, and take a look in the mirror and decide what exactly it is you want to work on.
As far as your training split goes now, the only thing I'd add to the upper body portion is a rowing exercise of some sort for the upper back, that will help to anchor the rest of your lifts, and give you more stability. Also, throw some roman chair sit ups or good mornings in there for the lower back. I'd get rid of either the triceps pushdown or pulldown (just pick one), as they really focus on the same muscles. When I do upper/lower split training, I like to put forearms with my lower body day, only because I find I can get a better workout in and my arms aren't burned out by the time I get to them. Cycle in different exercises for the various body parts, such as bench press exercises for chest(incline, decline, BB, DB, etc). With your lower body workout, straight legged dead lifts will help to work your hammys, and a calf raise of some sort would be beneficial. Also, look into adductor and abductor movements if you want some more in there. the best upper/lower split I've personally liked is monday and thursday upper, tuesday and friday lower. I assume that there is a typo in the upper body in your original post, and that you do upper on wednesday and monday. The one thing I don't like about this is that it doesn't maximize your rest time between workouts, but if you need to make due with the time it should be alright.
Anyway, good luck with the workouts, i'll check back occasionally and answer any more questions you may have (If I can).
P.S. as a side note I’d stay away from supplements at your age. I did and i’m glad, I believe its helped me progress as far as I have. the only thing I really took was a multivitamin, which really can’t hurt.