Terriers know the difference between squeaking babies and prey. Honestly, they really do. I've owned several of them. None of them ever tried to hunt babies and toddlers, not even the one who hated and distrusted small children.
Flexi leads are the work of the devil.
If you've never had a dog before I would start with something a bit more laid back than a terrier, unless it's a particularly calm for a terrier type terrier.
They're working dogs. They need to be kept busy or they will assign themselves tasks like standing guard in the front window to bark at passers by (my terrier is not allowed in the front room alone because of this), they need on average 1 hour - 90 mins walking per day, with at least some of this off lead, however their total disregard for recall training around prey makes this more difficult (mine is let off only in certain areas, only when I have time to wait him out if he spots a bunny to a chase and only where it would be appropriate for him to hunt should the urge become too much)
They love mud, they're very vocal and have a tendency to lean towards being a bit grumpy.
Mine is currently pacing the perimeter of the yard looking for trouble because of illness he's only been getting out for about 30-40 mins a day, the difference in his behaviour is notable.
If you can handle this they can make good pets in the right hands and are great little guard dogs and full of character, mine makes us laugh daily.
The issues you outline in this dog aren't massive and are easily solved with a little training.