Indeed, you should probably read up a bit on the way Shinto works. If you do so, you'll see that the word 'god' usually used in English translations is, despite being arguably the closest word in the English language, not really entirely accurate. If you want to have a discussion on this, you need to first decide what the word god actually means. Although if you accept the standard definition (the definition of 神 [kami]), you'll find that most of your examples (women and children becoming gods etc), are hardly that strange. Technically, everybody becomes a god when they die anyway.
But yeah. Start by looking up the terms 神 [かみ, kami] and 八百万の神 [やおよろずのかみ, yaoyorozu no kami], and getting a good understanding of what they mean. That'll help your understanding immensely.
Playing Touhou might also give you an interesting pop-culture perspective on the matter of Shinto gods in general. Sort of. Maybe. And I also second the suggestions of Kami-chuu and Kami-sama Hajimemashita as good examples of this kind of anime.