So I bought it the weapon skill, and just for the heck, and the cheapness of it, the shoot skill as well.
Now, my alchemist died at char level 22 to the high tempest, sadly. It was my most succesful character ever, unlocking reavers, cursed, chronomancers, yeeks and the Infinite Dungeons in one run

It does leave me with some questions:
My golem had 2 generic points. Don't recall if it had those from the start, or gained them at level 10. It didn't get any more at level 20 in any case.
Does a golem ever acquire any more than 2 generic points?
Also, is there anything specific those should be saved up for? The only (useful) skill in the weapon combat tree that doesn't seem to scale with the alchemist's golem talents is the weapon skill that gives + to attack. I'm not sure how far up the armor skills, and the weapon damage skill will go with maxing the alchemist's golem talents.
And another one: if I am controlling my golem, when completing an escort quest, will it get the talent (tree) instead of the alchemist? That could be interesting, and fun.