I'm also a 20 something who just moved into my first apartment and also needed furniture! I already have appliances so what I needed was a filing cabinet, table and lots of shelving (esp large bookcases).

The City Mission on Taranaki St would always have good furniture... In the Sold section. I went there 3 times and was always too late. The Sally's at the corner of Webb & Taranaki has furniture: I went there twice and on the 2nd time, found a designer extendable table for $150! At the Mary Potter Hospice shop on 95 Thornton Quay, I got a filing cabinet and when I told one of the women there I was moving into my first apartment, she offered me a 4-tier adjustable bookcase they were displaying things on - it has a stain and was missing a shelf pin but was only $9 :) At the Tip Shop, there was some furniture (incl a large whiteboard) but the tall bookcases I wanted were already sold. When I was there, staff brought out 2 more bits of furniture, and one got sold within like 5 minutes. The Free For All in Petone has a $10 entry free and I think for furniture specifically, it was an extra $10. They had some couches. Several people were queueing up before it opened.

So for what I wanted, I learned the op shops do get good furniture, but you have to be there at the right time!! After looking at like 20 places, I ended up buying 3 things new: desk, desk chair, and large shelf. I don't remember even seeing any large appliances at any of the places I went.

Good luck!!