I've just said which one or rather implied it - the Anschutz obviously, to shoot rats in the barn, the odd rabbit before they all scarpered, or a fox lurking in the farmyard at nightfall - "Dad only had to get the smell of a fox and he'd be out!"
Bamber had a zeroing-in session with AP and his new Anschutz didn't he? i.e. one fitted with telescopic sight which is indispensable when shooting any of the above.
Which was no doubt referred to as the gun ie "Sheilas gone crazy shes got the gun"

I'm not aware JB had a zeroing-in session with AP?
No the open sights aka iron sights which are built into the rifle at manufacturing are perfectly good for shooting vermin at a wide range of distances. JB was a marksman and no doubt when in the cadets/at Greshams/as a boy on the farm learned to shoot with open sights.
The fact a telescopic sight was fitted when purchased in Nov '84 and AP claimed it was fitted last weekend of July '85 isn't evidence it was routinely used. Probably the only reliable source to confirm one way or the other would be NB. Others who may have known are Jean Boutell the housekeeper and farm worker Len Foakes both of whom were regulars at WHF unlike AP.
AP was wrong about scars to JB's hand so it could be argued he was an unreliable witness