IMO fins make a huge difference to your efforts, also make sure you get your weight belt set right so you are not struggling to get back up, youtube it.
There are so many options for blades, but id go for an all in one to start in the $180ish range given your budget (or half that for used), almost all brands make beginner fins, just google them and check out which has the best amazon review etc. Then move onto pockets and composite fins onces your feet and legs are use to it, dont go too firm to start is all im trying to say.
If you know what you need, look for used gear on trademe including suits. If you are in the North Island 5mm should be ok all year round, although i feel the cold easy and am use to Aussie water.
The best advice I can give you, if you havnt speared before is find an experienced friend, someone who isnt a cowboy.
I got into it just because my uncles were scuba instructors and when I was a toddler they would have me snorkling around pinnacles, slowly I just got info from them in regards to not using tanks as they would usually free dive when not working. Then in my teens has friends who were into it. So I learnt mostly from other people.
Never go by yourself, never have friends you feel embarassed to ask questions too, never dive beyond your limits, make sure you where a watch.
Id advise getting a gun over a pole. But before either Id just go free diving and learn how to snoop up on fish. Getting a gun is a big part of the fun for a lot of people. Conversely a lot of people love the hunt of a sling.
So to sum it up, join a club or some friends, ask them what you need to buy, then buy used gear but check it out before you buy it.
Something like this might be a good start, these beuchats are known for being easy on the ankles etc. And then either change the blades to the blacks (competition) or get into Ruku when you get more money. I think they are about $180nzd..... if you look around, or much less used.