The rapier is a bit erratic. The most powerful melee weapon you can use one hand that you acquire after dungeoneering for a few hours: you need RS gold at least 80 dunge to buy it through the dunge reward system. The most chaotic weapons are among the most powerful in their field.
Bandos chestplate and tassets. Falling in price, these are the most popular items to buy in the event you're able to pay. 12M for one piece and 12M for the second. They provide spiritual and strength bonus.
I'm no expert on helmets, however if you're killing you need the complete Slayer helm due to its extra bonuses (likewise Salve amulet if it's relevant) and Verac's helm if not.
If you're looking for boots you'll prefer the dragon. There are some better boots that are known as "ragefire" I think, but I don't think buy Runescape gold you'd want to invest your bank on them. For gloves, choose barrows gloves from RFD or potentially an goliath glove made from the dominion Tower.