Hi freom Taranaki

Welcome!

Can ask here, or the general discussion area. But, youve already spolied yourself with Weihrauch theres a lot of guns out there thatll be a downgrade! 

Weihrauch and Air Arms are top of the heap - Weihrauch having most options vs Air Arms with their TX200.. It all comes down to budget really, and also if you have a license.. If you have FAL then PCP is a great option as they can be very quiet with good power and easier to shoot more accurately (not necessarily inherently more acurate, just easier to use) 

For rabbits an HW95 would be great, HW97 if you want to get into some target shooting as well, HW80 if you have a bit of a possum problem as well. 

Diana used to have some good offerings, theyve slowed down a bit, but if you can find a Diana 340 Ntech that'd be a good option. 

Cometa fusion is a good more budget friendly option - spanish made but a big step up from gamo etc, cold hammer forged barrels are accurate, the trigger is very adjustable and can be made excellent. My preference would be .177 with JSB exact heavy pellets - I had one before my TX200 and could group just as well. 

Budgeting below the fusion, id say keep saving... i may be a snob but if you like quality then better to buy once. 

But, a cheap crosman / benjamin will do the trick, but you need to master the trigger etc otherwise youll not get best accuracy. dont bother with the multi-shot springers - the mechanisms break. gamo is overpowered and use far too much plastic