There is no true anwser for what is the best weapon for you. It largely depends as well on the situation and the preference of the user. But as for a simple guide I can assure you with what I know as a long time user.

1. Chaotic Longsword: requires 80 dungeoneering, 200k tokens and needs to be recharged.
2. Chaotic rapier: requires 80 dungeoneering, 200k tokens and needs to be recharged.
3. Abyssal whip: one of the best weapons is great with training attack, also fairly cheap.
4. Abyssal vine whip: a little stronger, more damaging special attack and delivers poison.
5. Dragon Longsword: requires a simple quest and has a good special attack.
6. Dragon halberd: can hit opponents 2 squares away.
7. Obsidian splitsword: comparable to a rune sword but does 20%+ damage with a Berserker necklace.
8. Korasi's sword: one of the best PK weapons with its magical special attack which hits hard and never misses.
9. Keris: is a dagger obtained after defeating the Giant Scarab at the end of the Contact! quest. Very effective against kalphites.
10. Dragon dagger (p++): does not do much damage normally, but has multiple uses of special attack which hits twice, and poisons.

Note that the Chaotic longsword is the singular strongest one-hand weapon in RuneScape other than some gorgonite, promethium and primal weaponry which could only be used while dungeoneering. However, some players prefer the Chaotic rapier as it hits faster.