I chose Weight, Shape, looks, and just like it but I break it down a little bit to show how that has changed over the course of 4 years playing/buying yoyos.
My first 2 years of yoyoing I purchased about 30 metals, and then narrowed it down to my favorite 3 and sold the rest. I kept my Sleipnir, Chief and Nessie and didn’t purchase any metals for 2 years until yesterday where I chose an X Cube Teh Yo and 3 yo 3 Bass Line 2. The Nessie I gave to my daughter but still play so I count that as one.
There was a general trend towards performance in those first 4 years. Counter to the traditional view, my general philosophy is that whatever increases the rate of repetition increases learning at a greater rate. I have personally found it effective in that I learn tricks on bearings, and then usually have to make little effort to then perform the tricks on fixed axle. Ultimately how you practice is how you will perform. If you focus on being smooth, it doesn’t matter what yoyo you are using. The tool can make a difference, but IMO nearly as big a difference as your focus and habits.
Now my two recent purchases are geared towards fun as my skill levels have increased to the point where I can play with whatever yoyos I want without getting frustrated because I know I could do this on another yoyo. Also weight is important as lighter weight means playing longer.