222 Remington ammo is about the same price as the Hornet. The .222 has better ballistics than the Hornet. Hunting ammo (premium) for the .357 is maybe 3/4 the price of the 222 basic hunting ammo.
.357 is normally about a hundred yard round. The .222 or the Hornet is double that before it starts to fall off some.
I've got two Stevens, one is a 20 gauge .222 Remington combo, the other a clip feed bolt action in .222. Both were under $250 used, both are very accurate. The .222 seems to do the job well, it will take down most anything under 40 lbs. reliably.
A side note on my Stevens bolt action, the barrel is about shot out. The lands are well worn and it is still accurate.