To make it short:
the best way to level up is getting the needed components from Philosophers Caches and making other components from them.
Both the Philosophers Caches and the Recipes can be bought from The Bifrost.
The right recipes can be quickly found, because their prices are multiples of 1000 gold
(exactly 1000 times the recipe level)
Always use recipes of your actual level (may become expensive because of low success rates)
or one level below (lower experience gained, but can be good anyway because of higher success rate);
for lower-leveled recipes, you won't get any more experience.
Alchemy Shop (sorted by descending Prices, so most of the fitting recipes are on page 1):
http://www.gaiaonline.com/gaia/shopping.php?key=awerynsdfnicvbia#?tps=all;1;pricedesc
To find the right cache to open for a specific component, you can use this thread:
http://www.gaiaonline.com/forum/gaia-item-alchemy/what-makes-what-a-guide-to-the-use-of-components/t.75169525/
Some components should be saved instead of selling them,
because they will be needed for higher-level reactions.
These components are (no guarantee of completeness):
Bottled-up sunlight
Bottled-up moonlight
Ectoplasm
Red Mercury
Sunstone
Moonstone
Uranium Biscuits
Ambrosia
Quantum Particle
Spice
One additional hint for Level-4- and Level-5-Alchemists:
Try to handle with a more advanced Alchemist (Lvl 6 or above) to get Ogre Bones for a good price.
With only one of them and some additional stuff from the shops, you can make a Deluxe Bone Mask.
One additional hint for Level-6- and Level-7-Alchemists:
Make some Ogre Bones. They need only a few ingredients and are good for rushing through the two levels.
Then look for offers from lower-levelled alchemists
(They are really easily made; any offer above 1 million for each bone is a good offer)
...and one last hint for Level-10-Alchemists:
Congratulations, you've done it! But there is still one thing you can do:
At the moment, when you reached level 10, you've been sent a very special recipe, for the Crown of Thrice Great.
Most of the stuff which you need for it can be obtained again from the Philosophers Caches.
One exception is that you need 10 Aspiring Alchemists.
This may become very hard, because every player is able to make only one of them.
But when you finish it, you can sell the Crown for a lot of money.
500
100
50
