Kiwi Rail

It's been several years since we did the TranzAlpine, but I would say to you that we were pretty underwhelmed by the experience. Rather than spending a long and tiring day on the train why not just rent a car a drive the route, which parallels the train journey for the most part, and thus give yourself the freedom of movement that a car provides - can't stop for photos at a wayside pullover on the train.
We frankly didn't think the TranzAlpine was worth the money...and wouldn't recommend it.

Although I did not personally take the train, I was on a hop-on/hop-off backpacker bus that made a stop in Greymouth and picked up a group of backpackers that had elected to take the train from Christchurch as an optional excursion. Similar to the previous poster, the majority of those that did this option seemed to think it was not particularly memorable or worth the price. If you don't want to drive or deal with the expense of a rental car (particularly if you happen to be traveling solo and can't split the costs), you could look into taking a bus. The bus system for the general public (not the backpacker circuit buses where you would need to buy a pass) is pretty comprehensive, covers a lot of routes and is very economical. It's not going to make photo stops along the way, but you can always just relax and look out the window - same as you would on the train.

Man in Seat 61 has a detailed explanation on how to get the best fares by calling---although they may not be offered if they know you are calling from outside New Zealand. He also explains a computer workaround so you computer's location cannot be identified.

We did not try either; I simply bought our tickets for the coastal train on the website. I got the lower of the two fares offered,although not the lowest ones offered to New Zealanders. We were happy with the fare and enjoyed the trip up to Picton.