I have done some beating and have been told that shot sizes No. 4, 5, 6 and 7 may all be used by the Guns on the same day.
The size of shot is, of course, a matter of personal choice and depends upon where you are shooting and also what suits you and your gun.
Personally, I now tend to lean more towards No. 5 shot, as the heavier pellet is more likely to kill cleanly, though you will have fewer pellets in the killing pattern.
I also prefer No. 5 shot for pigeon as, again, there is more stopping power and penetration on these tough little birds.
Sadly, time and again I see Guns treating pigeon with utter disrespect by shooting at ridiculous ranges, likely only to cause wounding even if they hit them.
Whatever size shot you decide to use, try and minimise wounding.
Do not shoot at a living creature beyond the capability of yourself, your gun and your cartridges.