Well I don't suffer from allergies, but my husband does... more so with cats but he has never had a problem with our vizsla or lab for that matter. My boss used to break out from the hair rubbing his arms, but that went away too. There really is not truly hypo dog.. It may be best for you to just find a Vizsla you can spend some time with and see how it goes. That probably is your best test, so ask around and see if someone is local. Or look up breeders near you and go have a chat, which I totally suggest as well.
As far as exercise... they need it, crave it, must have it if you want any peace. I did TONS of research before I chose this breed... I have been in the dog world through personal pets, then work for quite a few years... and I still questioned whether I got the right breed those first 2 years. I started out with her before I had a job, then went to a job I could bring her to (to play with other dogs even), but it was still hard. But you put your work in those first couple years and then things hit a stride. When she was a 11 week old puppy we would hike (on long line dragging) for 1-2 hours several times a week and I would say she could do more if I had let her. But it kept her happy. Add to that having 5 acres and woods near the house to go explore too. She still needed more to settle. They are not the sort of dog that will be happy with just leash walks, they need to RUN and hunt and explore. So make sure you live in an area where you can provide that. And jogging does not qualify either, sure it is better than nothing but they need to run at their own fast Vizsla pace too, not just a humans. And at DIFFERENT locations not the same one all the time.
The other almost BIGGER need for them is MENTAL stimulation. They need to be taught how to relax, best way to do this is with brain engaging games/activities. Luna will come home more tired from an hour of working on agility than if I had hiked her for 3 hours. Because she was mentally exhausted/fulfilled. So you must have the time and means to engage their brains.
As far as fencing, my dog can easily jump 4 feet at a standstill and she is one of the smallest Vizslas I know. So a secure fence won't hurt, and gives you peace of mine as nothing can get in to harm her either.
Mine has also been trained to an invisible fence and it works beautifully for her (and the other 7 hunting dogs that live here). Luna has prey drive and a half and notices anything that moves. After she was trained to the fence she actually broke through it one day to go after a rabbit, but broke BACK through to come back to the yard. So she got herself a correction twice over a rabbit but still came back. And has never even thought of crossing since. Now she is a smart cookie, so i can't say this would be the same for any... but I know many types of dogs and breeds of dogs who hunt and don't hunt who happily can live inside an underground fence when you are home, with proper training. i still bring mine inside when I am not around as it does not keep other animals out.
A word about invisible fence and then ecollar training... I find it much better to do any ecollar training before the invisible fence. We deal with a lot of training dogs who know the invisible fence and thus ecollar training can be a lot trickier... as they have learned that the stimulation means "don't go there, back up" when really if you use it to call them to you it can become counterproductive if they relate it to a fence. I trained mine to fence after the ecollar and it worked out well, but simply taking your time and working in all sorts of environments allows them to learn it's a different setup over time. But just a thought.
It all comes down to knowing your dog. I say stick with your immediate fence for potty breaks and then work on some recalls so you can take advantage of the park land behind you. Most vizslas will not be happy in their yard every day anyway, so you will need to get them out anyhow.
Keep asking great questions, and try and find some local breeders near you as they can be wonderful assets too. Keep in mind, IMO a good breeder will question YOU about why you want a Vizsla, not try and sell you one. Breeder should be picky, as they want to make sure their puppy is going to a good home.