What is your most preferred way of modeling objects from scratch?

I find myself using the 2D, background image technique the most. Where you start off with a flat square, extrude it to fit the 2D view, then start creating a rough 3D shape, and piling edge loops to give it more definition. This way I’m come to find sometimes works, but sometimes leads to a giant mess of misshapen lines.

What’s your preferred modeling technique? Which one’s the quickest? Which one gives the cleanest looking mesh?

You need learn to think in terms of volume not 2D. Many people have this problem. A sculptor constantly checks his/her sculpt from different angles. They don’t just carve from one view and then check the damage at the end. Many beginners also have a tendency to work on details before ensuring the overall from is correct.

Unless I’m modeling a flat object I always check how it looks like from the front, side, top and perspective. I always move verticies in ortographic view and check every change in perspective. There’s a number of things I constantly need to juggle like “does this look correct from all sides?”, “is my edge flow correct?”, “do I need to correct for lens distortion in reference?”. You just need to spend a lot of time modeling different things and eventually will ease into it.