So, you've tried the queso blanco cheese, and want to crack on with another one. There are a few variations of queso blanco which use a food acid to coagulate the milk, but to really get going with more advanced cheeses, you will have to find a source of starter cultures. You’ll also want to extend your basic equipment so that you can dedicate some exclusively to making cheese, especially if you are using raw milk. It's just much easier for the proper sanitation. Your cultures won't perform as well as they should, and possibly not at all, if contaminated.
Most people start out with smaller batches of cheeses, so a stainless steel pot with can hold up to 8 liters is a good place to start. You will also need an accurate thermometer which starts at least at 0 degrees Celsius, as many cheeses won't be heated above 35C. If your cheeses are failing time after time, but either not coagulating or not draining enough whey, your thermometer is probably not accurate; even as little as 1C can cause a cheese to fail. Test it against a known temperature, such as that of boiling water. You will also need a stainless steel or plastic colander or strainer, which can sit up over the container into which the whey will drain. A medium-sized sieve with a handle is a very useful item to have, and saves the inevitable mess that pouring out the curds and whey can make. You can purchase a cheese knife, which is a blunt-edged blade specially used for cutting curds, as it won't mark up the insides of your pot, but you can simply use any knife which reaches the bottom of your cheese making pot.
You might like to invest in some cheese moulds, but there are a lot of kitchen containers you can convert into what you will need, as various cheeses have moulds that are specific to that type of cheese. Food-grade plastic storage containers are a good starter mould if you heat an ice pick or similar and melt holes in the sides, to get good drainage. Have a look around the internet at the various moulds, and see what you can whip up at home. Once you figure out what your house speciality is going to be, then you might like to purchase the 'proper' mould. However, most moulds used are based on tradition, so whatever works for you should be fine, and will probably enhance the 'rustic-look' homemade cheeses. For a hard, aged cheeses such as a farmhouse cheddar, you will need a cheese press. There are a number of them available for purchase in New Zealand, but if you do your homework, you can make your own quite handily. Just make sure that it's large enough or small enough to hold the amount of curds you will be making, and most hard, aged cheeses need to be above a minimum thickness, or they will form too thick a rind in relation to the eatable cheese within, unless you wax your cheeses before they are aged. Consumables, such as starter cultures, bacterias, wax, and enzymes such as lipase, are all available in New Zealand, but it is also perfectly legal to import them from a commercial supplier. Most cheese recipes will indicate what kind of press or mould you will need.
Cheese making equipment may seem expensive at the start, but it's really a small investment for the well-equipped Cheese Maker, when you think of all the years you will be able to use your gear to make your homemade cheese!