There actually is no best weapon in my standard... But I am sure others would the think the Blade of Bliss would be. If you would give us information on your level and class, this would be a much easier question to answer.
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The best weapon is to cut people
The overall best weapon is the Plasma Cutter. This is the first weapon you will acquire in the game.
you have to go to the merchant but do not click him then you say "hi, best weapon please"
Well if you need a ranged weapon it is the bow and arrow, but the best melee weapon is the diamond sword, made with a stick with two diamonds on top.
The overall best f2p Runescape weapon is actually a range weapon - Maple Longbow (sighted). It has a range bonus of over 100. The best f2p degradeable weapon is the Gravite 2h. Both are Dungeonneering weapons and need 45 Dungeonneering levels.