Instead of +Str to damage, you could just use Str for the weapon requirement.
I.e.
Daggers: 1d4, no requirement
Short Sword: 1d6, 13 Str
Longsword: 1d8, 15 Str
Greatsword: 1d12, 19 Str
Do the same for shields
Buckler: +1 AC, no requirement
Sheild: +2 AC, 15 Str
Tower Shield: +3 AC, 17 Str