For best success this is what I would reccomend. If you are mainly planning on surf fishing, then get a cheap surf combo at least 12ft, then all you need is a few ledger rigs with 5/0 hooks and a couple breakout sinkers. You’ll catch pretty much everything on a ledger rig and whatever bait you can get will work (squid, bonito). For Rig sharks crab works best.
If you’re heading to invercargill the best place to fish there is off the Bluff Wharf, where you can catch Blue Cod, Red Cod, Warehou, Salmon, Terakihi, Skate, Rays, Sharks etc It also allows you to park your car right on the wharf without having to walk any distance.
Pretty much all the beaches along the East Coast between Kaikoura and further south to Dunedin are very similar in terms of species of fish caught, all have a lot of sharks (dogfish, school sharks, rig sharks, seven gillers, elephant fish, carpet sharks) and fish species like Red Cod, Kahawai.
Off the Wharfs at Bluff, Dunedin, Timaru, it is possible to catch Salmon.
For any fresh water fishing you need a license, and it’s not really worth it for just catching trout and salmon (Which you can get in the sea anyway), plus you need totally different gear.