Shooting pigeons and hosps is one of the reasons I got back into airguns. For refference, the longest shot inside my sister's barn was 22 yards. Most shots were around 10-15 yards. For pigeons I found my modified Crosman 2260 shooting wadcutters or Crow Magnums at 12fpe was more than enough to humanely put them down. For hosps I used my .177 6fpe Crosman 2400KT and wadcutters. Both these guns are very quiet which really helps, however they aren't much good in the cold. During the cold months I used my .22 Brocock Contour (the gun in my avatar) shooting Crow Mags at 15fpe.
I also kept my .22 Daystate Regal outside for when they would smarten up and fly out. Once outside they tend to sit in the trees or atop the outbuildngs putting a higher powered gun to use.
This past August we spent 3 weeks at our daughter's in upstate Montana. Her in-laws own 2 large ranches and a farm and asked me to help with the pigeons. I only had my .177 HW100BP-K with me, but between myself and my son in law shooting his .22 Benjamin NP, we littered the ground with pigeons.
Something I've witnessed. We all know headshots will produce a lot of wing flapping and rolling on the ground. That disturbance can scare off birds. I've shot many more when taking them with heart/lung shots as they don't put on much of a show. With less meat for the pellet to penetrate, I prefer a well placed shot to the center of the back than the front, though inside buildings they rarely present us that shot.
Whatever gun you decide on, good shooting and have fun!