What is the best sword on runescape for nonmembers?

"Best" depends very much on context. Theoretically, if you have the money for it, you can purchase Christmas Crackers and Blue Partyhats. The "best" armour and weapons are part of the Corrupt Dragon equipment group, but these are very expensive and degrade quickly into dust. The most expensive conventional armour available for free players is Saradomin armour, though it has the exact same stats as regular rune.