In your situation I'd be looking at the Jack Russell. Beagles are bastards to train and the stock in NZ is not good. MPI had to get their stock (for detector dogs) from Australia initially as the NZ stuff was just too belligerent for their training methodology.
Visla's are great hunting dogs, but probably too big for your purpose. This won't be popular, as it goes against many comments here, but I having worked with more than a couple of dozen Vizslas and personally believe the Vizsla is no more a "Velcro dog" than any other soft breed. The problem with Vizsla's is every bloody breeder tells people they are getting a "Velcro dog" and then some behaviors are encouraged that normally wouldn't be. Pushing, clinging, crotch sniffing and other examples of bad manners are tolerated because they are "Velcro dogs" Load of rubbish. Every one I have worked with was no more clingy or Velcro than any other dog I have seen and once you took away the excuse give by the breeders they learned perfectly acceptable manners just like any other dog. As for not wandering... fences stop dogs wandering, not genetics.
I've seen lots of very competent terriers worked on deer... and they are great little characters. The only downfalls are they require very astute possum aversion training. Not really capable of grabbing and hanging on to a wounded big game animal, but they'll always have a go and they only warm very small areas of a sleeping bag!
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