I recently got a Kalphite slayer task, and since I hadn't visited the exiled kalphite colony, I decided to do so; the Exiled Kalphites are actually quite fun, and apparently converting the chitin to scraps is semi-profitable (or at least that's what the wiki had lead me to believe) so I'd really want to be able to get the necessary level ASAP, only 160k exp. Shouldn't be too hard, right?  So what would be the quickest way to 60 from 51?

There are several possible ways you could do it. Perhaps the best way would be to smelt gold bars from the ore using Lumbridge bank chest and furnace. If you have the goldsmith gauntlets from the Family Crest quest, the experience you gain is increased substantially, up to 56.2 ea according to Wiki. Also using numbers from there (note: I don't know how accurate these are, but as a ballpark it seems accurate at a glance), it will take you about 3 hours, at a cost of somewhere around 250K. Not bad huh? You should be able to recoup it with chitin scraps anyway.

 

Other methods could be using Artisan's Workshop with iron (i) ingots or citadel smithing, but I don't think you would find them as appealing given your objective is to level up quickly. If you'd like me to elaborate more, I wouldn't mind though. Hope this helped! :)

First of all thanks Arceus; gold Smithing looks like a decent option, though I'd need to grind out 4 magic levels for the quest, which can be done through superheat item, netting me a head start, sounds tempting, but I'd need to add the cost of nature runes to it.  

 

Artisan workshop is semi-AFK, which is a big plus, but yeah it is slow. Citadel needs a clan, which is a problem as I am not in a clan :P. 

It depends on your budget in both time and money then I guess. If you don't mind sacrificing the better part of a day AFK at the workshop or a good chunk of money doing straight up smithing you can do that, but I'm not sure what you find preferable. If you're planning to superheat, iron appears to be the cheapest by a good margin. Unfortunately they're all loses aside from rune these days. RS WIki has a nice table here compiled with current prices.