Deadlifts work 70% of the muscles in your body, including your forearms and gripping muscles. Your best bang-for-the-buck to help your strength and get in some exercise is to pick heavy stuff off of the ground a few times.
Rather than someone interpret this as "do deadlifts over squats" I'd say "do both because they're both great for your body if executed with proper form and weight."
Heavy lifting and trying hard is important, like you say, but it's a relative thing to experience, genetics, age, etc. I've seen grannies pull 1.1x bodyweight and I'd say they were lifting "heavy".
Also as to what is a heavy amount of what is a light amount - its irrelevant to an individual. You should lift the an amount that pushes you beyond what your comfortable with, but not so much that your risk injury.