In a game with a minimap, what factors should be considered when choosing where to put the minimap on the screen HUD? What choices are typically made when wanting to emphasize a particular factor?
There's no clearly "most common" position beside one the four corners. If you an information band/ribbon/... you typically want to embed it in your information ribbon, and leave the viewport as clean as possible. Since it's usually one of the biggest and more visual element to display in a HUD, you often want to push it to the corner to avoid it to be too distracting/overlapping. The band, when there is one, has often been place on the bottom, so it's no surprise, the minimap is often on the bottom left or bottom right in many games, especially RTS. Here is Dota 2 and league of legends:
But other games have the band above, so the minimap is above. On binding of isaac, it's on the top left
Other have the band on the left or right, so the minimap is on the left or right. I can't remember a recent game with a left band, so here is populous : the beginning, with the minimap top left.
If you do not have a band in your HUD, put it where it hides the least interesting part of the viewport.
However if your minimap is very, very important and you cannot go around without, you can center it on the top or bottom edge of the screen, like star citizen or elite dangerous (which besides embed their minimap in the game world).
Without knowing what kind of game you want to make, that's all help we can give.