The main lifts that add functional strength are: squats, deads, rows, clean (or some variant) and bench/incline.
That being said it's all about leverage. Strength vs Strength is only equal in equal position. It's all in how it's applied. Core strength is everything, it's how you do anything. Your body is basically in two pieces, and your core is the connector and the more conditioned and powerful your core the better functionality you are going to have. The amount of energy you can transfer into shooting or even a punch greatly depends on your core strength.
You ever see a guy in the squat rack curling? His arms are twice as big as mine, just rippling with muscle and veins. What are the odds this guy can hit anywhere near as hard or fast as I can? Probably not that great. At the same time I've man handled guys bigger and stronger than me and I've been tapped by someone smaller.
I keep thinking about marquardt vs sonnen