I was just wondering if I was modeling a triangle, let's say, should I use a quad or a tri? I often find myself in this situation where I'm not sure if I should leave the unnecessary edge or remove it and save some geometry.
You should definitely not put an edge where you do not need one. We model in quads not just for the sake of it but for many reasons like, for example, loops that form while modelling this way and the ease to select and work with them. If there is no reason to have a quad, there is just no reason to have a quad. There is no need to be afraid of triangles or even n-gons. N-gons for example may even produce nicer bevels in some situations then a mesh with loads of unnecessary edges with sharp corners. They can also be a huge pain and a source of rendering errors in other situations same as triangles can be a nightmare if you need to adjust a complex model but in other situations there is just no point to be avoiding them. If you know which situation is which it's perfectly fine to act accordingly.