It is so funny that you ask that! My DD and I do puzzles together all of the time and we have different approaches which make it sometimes funny and sometimes annoying to each other.
We always start out the same way-- we sort all of the pieces so she can start edges. That is where the agreement seems to end. She likes to sort similar colors into separate plates. I, OTOH, prefer to look for visual similarities so I like them spread across the table to scan. So we have sort of fallen into a compromise that we sort everything onto the plates then I grab a plate and work from there.
When I get big chunks, she is able to put them into place. We both agree that my husband's analytical process is not always helpful. He will find random pieces and look at the box and put it where it should be. Unconnected to anything. Just floatin' out there...
We usually do 1000 piece puzzles and have done a 2000 piece one once but my table to really too small to do anything that large if we want to eat.