This guide makes the assumption that you, the reader, are living in New Zealand. I will be referring to a few New Zealand services and platforms, but for any international readers from other countries, I would highly recommend getting to know sites such as eBay (USA, UK, Europe), Craigslist (USA, UK) and your local PC shop that sells Ex Lease machines (this is very important)
The difference between business and consumer machines is simple. Business machines, built for enterprise environments, are usually much highly quality than what you can normally get at a consumer store. This is (probably) because companies that buy these business machines in bulk expect some good use out of them - they would stop dealing with a brand/supplier if their machines kept failing.
I would normally default to recommending people buying a Thinkpad as a secondhand machine (laptop). Thinkpads have a very good reputation as being reliable, solid machines with many parts still available to buy (keyboards, screens, batteries). Consumer machines will often become discontinued after a few years, so it becomes next to impossible to fix and/or upgrade them down the line.
The Thinkpad "T" series are the medium-sized 14-15 inch laptops and are the most common. The "X" series are smaller, ultraportable laptops that usually have 11-12 inch screens. Finally, the "W" workstation series are the most expensive, with screens usually about 17 inches big and aimed as a desktop replacement machine.
All of these Thinkpads pop up secondhand on Trade Me fairly regularly (every other week). T and X series laptops will usually go for $250-400, whereas the W series will go for $500+. Thinkpads made after the Intel Sandybridge era (T420 onwards and X220 onwards) use chiclet style keyboards, which are okay but less tactile and nice to type on that the older generation keys.
Whatever you do, do not buy any Thinkpads that are Edge or "Y" models - these are tested to the same standard as the T X W business machines and will not hold the same level of quality.
If for whatever reason you can't find a Thinkpad that you like, I would also recommend looking into Dell's Latitude line and HP's Elitebook series. Both are business grade machines, with fairly frequent ex-leases appearing on Trade Me every other week for $150-300 depending on the model.
With any machine you buy, spend an additional $50 and get yourself an SSD. It will run faster, quieter, and produce less heat!