Str to handle big weapons, Int for skill points, End for lots of implants and Luck for criticals and easy casino gambling
There are no "big weapons." There are only Guns and Energy Weapons. If it shoots bullets, shells, rockets or grenades, it is a gun. If it shoows lasers, plasma, or fire, it's an energy weapon.
You can pretty much wield any gun in the game with a STR of 3 or more. STR doesn't affect GUNS, but melee/unarmed. The only thing you need STR for in a firearm character is just so you can carry them, and like I said, nothing has a STR requirement above 3.
All the good AGI perks increase critical hits, really. But, it's not just for VATS that these come into play; your accuracy real-time is affected by them too.