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I'm currently level 84 Alchemy and this is my guide to getting to 60(find all recipes on FFXI MysteryTour):

0-6 - Tsurara
6-10 - Deodorizer
10-16 - Mercury
16-20 - Echo Drops
20-28 - Sairui-ran (Requires cooking skill at 11. This is a profit item, just put in the little cash requires to hit 11. You also can stop flooding the silent oil market, that used to be profitable ^^)
28-34 - Potion (I know this is a big gap but it can be done, the synth is dirt cheap.)
34-43 - Vitriol (Use treant bulb recipe)
43-51 - Holy Water (Dirt cheap after the rusty cap nerf)
51-60/61/62 - Mixture of Hi-Potions, Glass Fiber(8x flintstone recipe), and Venom Dust.(This is the best way to go about it because of scaracity of the number of resources you'll need. Plus, if you continue Alchemy, you'll need the venom dust)

There you go, 0 to your lower 60s. I didn't lose all that much money on this skill up route, especially since siarui-ran is about 2-2.5k profit a stack. This is a fun craft that really starts getting expensive after 60(just like all the others), so don't let the easy beginnings trick you. Good luck!

BTW, NEVER EVER pay more then 3.5k a stack for beehive chips on Midgard, I want the price to go down ^^