Runescape: F2P: 51-55 Magic Fastest and what to Alch?

So yeah, I wan't to get ready to get membership this summer and I my #1 goal for summer vacation is to finish Desert Tresure for Ancient Magic. The only problem is that I have a measly 51 Magic. I heard that one of the fastest ways to get 99 magic is High Alching. I only have 51. So can anyone give me ideas to get from 51-55 Magic the quickest in F2P. I have about 1.3million on me so far and fishing lobs to make some more. Also, would you mind giving me some items to alch losing only the lowest amount of money in both F2P and P2P.