All players wield weapons in their right hand, (with the exception of defenders, which are wielded in the left hand, or shield slot.) or, if they are wielding a 2H (two handed) weapon, in both hands. If a player is using a two-handed weapon, they may not have any items equipped in the shield slot at the same time. In the case of thrown weapons, which are stackable, multiples of the same thrown weapon may be equipped in the weapon slot at once. A player may also equip a pickaxe or a woodcutting hatchet in the weapon slot so that they may hold more ore or logs, respectively.
These weapons are more commonly used than the other weapons available, because they do not degrade or break. Most types of basic weapons come in eight different kinds of metal.
Most weapons have a primary mode in all three styles and a secondary mode in the aggressive or controlled style. The secondary mode is normally weaker, but may be more appropriate to your target win.
Chainmail armour is weaker against stabbing; platemail is weaker against crushing, while the slash attack is highly effective against cloth, leather or unarmoured targets. Against monster hide, the most effective style varies. The only absolute defence against a particular attack is theProtect from Melee prayer(which has 100% chance of success), or the occasional NPC that requires something special to kill them, so you will still hit with the "wrong" attack and weapon, just not as often and with less damage (or not even at all, in the case of monsters like vampires).
The whole idea of having multiple weapon types is that one weapon type should not be all-conquering, or there would not be much point of having the others. Overall, though, popular weapon types for each style are:
Stab
Slash
Crush