Compound exercises are exercises that use many different muscles at once. The 4 major ones are: Bench press, squats, deadlifts and overhead press.
Getting good form on these exercises + standard push and pull exercises (chest presses/flyes, lat pulldowns, dumbbell rows, military presses, side raises etc.) is more than enough to keep you going for about 9 months.
and bodybuilding.com has tonnes of routines for beginners, just dont get lured in by the sound of crazy and whacky exercises. simple things work well.
Also, I was very similar to you when I started 3 years ago, 55kg, 168cms, 17% body fat and I ate like a pig but never gained weight. training upped my metabolism, but the real key was to eat frequently, even if it was in smaller portions. put something in your mouth every 2.5-3 hours. Good luck!
EDIT: I'm not a fan of weight gainers, they're usually about ~25% protein and the rest is carbs and sugar. I'd rather have a standard WPC shake and eat some rice or pasta.