First of all, in-game models always end up being triangulated when finally placed and rendered inside the game engine. So it's best to keep that in mind whenever you are modeling.
The best thing to do is start with quads and then optimize by later triangulating and reducing the areas that need to be optimized based on your polycount limit and such.
Quads always are best for animated/deforming meshes used in skeletal animations and such, which is one reason why you start out with quads. Then when you optimize and reduce areas that need it, you need to smartly reduce joint/deforming areas so that when a bone bends it doesn't create jarring results due to not having enough divisions (in loops around the joint).
Basic rule of thumb: if the part doesn't bend, optimize as much as possible (without reducing major contours/silhouettes). If it does bend, give it a few edge loops and be on your way.
For super low poly irregularly shaped static meshes like rocks, flowers, etc., feel free to start with triangles or quads, however you want. It's all based on your needs, the distance away from the camera (or height in pixels it'll be rendered for Level-of-Detail), the target consumer range (high-end gaming/middle-range/low-end hardware), etc. As an artist though you should just be given a polycount limit, texture limitations, and then be able to model based on those specs and whatever medium of concept is provided.
