Which magic schools should I choose for the late game? Or should I go for a specific artifact?

Do you think it makes sense to build an artifact smithy in the first or second week? In general, earlier? Make 1-2 level 1 amulets and give them to the golems. For speed, for example, or initiative.

It largely depends on how your hero spent those one or two weeks and what level they have reached (we are most interested in the "Knowledge" parameter);
as a rule, in the early stages of the game, there are well-known problems both with resources and with the order of construction - it is quite possible that it will be more important to build a Capitol or a Castle, for example, than a smithy...