The obvious choices need to be held as the standard. If I make a fighter and put the statistically "best" stat on Strength, and choose the obvious weapon of Longsword (because it's obviously a decent weapon), then I should expect (aka Obvious) results from fighting a basic monster (ex. Goblin).
that's a whole lot of assumptions, but it is a framework on which to compare other things.
Okay, so we're clearly on the D&D bandwidth for this. I'd rather we weren't, but so be it.
By your preference then, if a "better" weapon exists, it should not be hugely better than the Obvious Fighter (ex Level 1, 15 str, 1d8 damage). If we got 5d8 damage out of using a Cloven BattleWidget, then that weapon has created an imbalance by most people's reckoning. especially if they both cost the same, have the same availability, etc.
By my preference, "better" would be entirely situational. By my preference, there'd be something like in Legend RPG, where all weapons do 1d6 + damage modifier (+ tier), are either melee or ranged, and then get three special properties picked from a list, all of which are intended to be roughly balanced.
Or you could look at Legends of the Wulin, where the weapons list consists of very broad categories like "sword" and "spear" and "flexible (chain/rope)", and the only ways to get a weapon with bigger numbers are to spend XP to buy a combination weapon (which anyone can do), or jump through roleplaying hoops to get a legendary weapon that gets better the more you use it in the way it was intended.
Or you could look at FATE, where a "weapon" is an aspect or a stunt that provides a situational bonus, and if it's not listed then your weapon is mostly fluff. (There are still ways to make it have an effect - a temporary aspect called "Disarmed!" for example.)
Now an inefficient selection possibility still exists, as in I can lead a horse to water, but I can't make it drink. If a player chooses to wield a sword made of stuffed animals that does zero damage, what are the rules supposed to do?
Make it magically (or mechanically) enhanced to not deal zero damage.
Make it do non-lethal damage.
Make it stack up "humiliation" points in place of HP damage until the target is too ashamed to fight on.
Make the player roll taunt or persuade in place of attack rolls.