Where I hunt rabbits, only about 5% allow for a carefully-placed shot; the other 95% have to be shot on the run.
As such, I go for the .22 WMR.
.22 LR is plenty of cartridge for a rabbit, but it doesn't work well with poor placement. When you add the fact that Black Tailed Jacks are often more than twice as big, twice as fast, and twice as jumpy as the Cottontails most people have in mind, the extra power of the .22 WMR is nice to have.
Cost isn't an issue. I paid 6 to 9 cents per round (over 10 years) for my stash of .22 WMR ammo, and I usually hunt with a 4-round magazine in the rifle. If I fire every round in the magazine... that's a whopping $0.36. Even at current unnecessarily inflated prices for premium ammo (Win Supreme 34 gr HP - $0.27 per), it would be $1.08.
On the rare occasions that I'm actually after only cottontails, I give up before leaving the truck or camp. Since cottontail-only trips only happen during big game hunts, the only legal weapon is a shotgun. Since the terrain I hunt in doesn't provide many shots within shotgun range... the shotgun is a waste of time. Conclusion: give up before you start (or go after grouse, instead).
.22 WMR - for power, range, and bullet selection.
"Such is the strange way that man works -- first he virtually destroys a species and then does everything in his power to restore it."