Let me put my 2 cents here, some peeps will probably disagree, but hey sue me
Practically you can go throu all game using only handful of spells so in that regard you do not need/want alchemy BUT, on my run with my Houdini I wanted to try most of the spells I had access to at highest level.
Alchemy is great at the beginning of the game when you can spend 17 or so crystals for phenix, blizzard or geyser instead of 35, the problem with alchemy is, it becomes obsolete very fast and you don’t have that many runes on the start to put in that skill you won’t profit later. If it had +1 to intellect with every level then that would be a must skill.
Crystals themselves, your first priority is to get 100 of them asap. I got lucky with wonderers spells (had 9) so your birdie will work overtime with making that ancient knowledge, well assuming that you get it, and every time it will cost you 5 crystals.
Skills… hmm… by the mid game you will have enough runes to max your magic tree
I would say higher magic would be priority, and then there is no wrong way to go since all the skills are benefiting you in same way or the other.