Usually Abyssal Whip for it's attack bonuses and speed, but Dragon Scimitar is good because unlike Abyssal Whip it can train your strength. Also there is a Saradomin Sword that is good because it hits better than a Dragon Scimitar but it can train strength as well.
Dragon claws
In my opinion the best is a rune scimatar
An Abyssal Whip, this weapon requires 70 Attack to wield, but this being the best one-handed weapon in Runescape also comes at a moderately-high price inside the Grand Exchange, especially to a new member.
Gravite shortbow.
vestas sword, but the best weapon is chaotic maul.
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.
the best weapon in RuneScape seems to be the Chaotic Maul, having an enormous max of 686(68) recorded. You can get the Chaotic Maul by obtaining 200,000 points in the Dungeoneering skill.
The corrupt Dragon 2h is best tradable weapon on F2p, although is degrades rather fast. The Gravite 2h is not purchasable with gold, rather Dungeoneering tokens, and also degrades, but is the best weapon in Free-to-play.
I think the Godsword is the best weapon you could get. Each Godsword has diffrent high hits but all of them are good.
In my opinion it is a mithril scimitar.
The best melee weapon for non-members is probably the Gravite Rapier, in terms of damage per second. The weapon with the highest accuracy and strength for nonmembers is the Gravite 2h sword, though this weapon attacks much slower. Please note that both of these weapons require you to dungeoneer for quite a while, especially if your combat level is 90 or higher.
armadyl god sword for two handed weapons and abyssal whip for a single handed weapon