I want to select the horizontal rings not the cross sections, but Alt + Left Mouse Button will randomly choose between either as seen below it selected the horizontal correctly but for the one cell above it selected a vertical strip.
Blender's Loop Select tool usually doesn't select "random" loops. To select a horizontal loop you have to Alt+LMB click on the vertical edge between two horizontal adjacent faces (yellow, see image below). To select a vertical loop you have to Alt+LMB click on the horizontal edge between two vertical adjacent faces (red). If you click more or less the center of a face because you were not aware of this functionality, Blender will choose the direction depending on which edge your cursor will be closest to.
You mean that sometimes it selects from top to bottom and sometime from left to right? Well, that is perfectly fine as it should be but you are doing it wrong, you don't have to select randomly in your face and expect it to select what you want.
This is whole functionality for loops selection