To freshwater fish in New Zealand you would need to buy a licence, they are about $90NZD for a whole season.
The best salmon fishing is probably in Canterbury. The size and number of fish in the rivers can be quite erratic over the course of the season.
The south island has many excellent trout waters. If you were only after trout fishing a good place to base yourself would be the town of Murchison. From there you are less then a hour drive away from around 5 highly regarded rivers, and less then 20 minutes from several.
For a combination of trout and salmon, the town of Methven on the Canterbury plains would be worth considering. The town is situated halfway between the rakaia and rangitata rivers which I believe have good Salmon runs. Methven is fairly close to the high country and good trout rivers and lakes.
It might pay to get the service of a fishing guide early on in your jounery. That should quickly get you up to speed with fishing for New Zealand trout. Your plan to base yourself in a single area for period of time would give you a good chance to learn the rivers and increase the chance of success.
With your bubble float idea, the New Zealand regulations limit the number of flys to 3 at any one time.