1. unsorted catches
2. second string team players, pokes to gift,and misc. pokemon that don't have any 31 IVs but are still quite good (mostly dittos)
3. pokes with more than one potential or confirmed 31 IV (potential 31s at the top, confirmed 31s at the bottom)
4. pokes with 31 IV in HP stat (potential 31s at the top, confirmed 31s at the bottom)
5. pokes with 31 IV in attack stat (potential 31s at the top, confirmed 31s at the bottom)
6. pokes with 31 IV in defense stat (potential 31s at the top, confirmed 31s at the bottom)
7. pokes with 31 IV in special attack stat (potential 31s at the top, confirmed 31s at the bottom)
8. pokes with 31 IV in special defense stat (potential 31s at the top, confirmed 31s at the bottom)
9. pokes with 31 IV in speed stat (potential 31s at the top, confirmed 31s at the bottom)
I haven't played much recently (I'm waiting for the new update to finally be ready) but I really enjoyed breeding, so my PC system is set up to maximize my ability to quickly find pokemon with certain stats I need.