Pretty much any rifle will work for vermin control providing it has adequate power and accuracy. Things that may swing your decision to one over another are :-
what type of vermin shooting will you be doing ? static, stalking, mix, indoor, from a hide ? if static a heavy rifle or long barrel is not much of an issue, weight maybe if stalking depending on terrain and a long gun may be impractical if shooting from a hide or vehicle
You're going to be using a Zulus, so you may want a rifle that comes with a picatinny/weaver rail as standard to save the hassle/expense of buying dovetail convertors - they can also add unwanted height to your head position, you will also need to be able to mount the Zulus far enough back to get your eye to the eye cup (and that's before disappearing down the MOA rail rabbit hole)
Likewise you may need to be careful to ensure you have room to mount the Zulus around any magazine or if single shot you have room to load with your fingers - bullpups can be easier in this context than say an S200 or Rapid
Then there's fit, balance and aesthetics all of which are down to the individual