I just use food storage containers from the equivalent of the dollar store here. There are plasticisers that will leach out of some plastics and are unsafe for food. Most of the problems I've heard about involve heating the plastic, but I still wouldn't use non-food oriented plastics. Other than that, I think anything will do. I suppose size is potentially a problem if you made a really big cheese. Advice I've heard is to choose a ripening box that is mostly empty after the cheese is in it. This is so that you have some air circulation. In my limited experience, I've had containers that were mostly full and some that were probably about half empty. The ones that are mostly full tend to have mould problems. YMMV. The closer the cheese is to the side of the box, the more humid it will be along the side, so you want to have something where the amount of space is fairly uniform if possible (i.e. a square box rather than a rectangular one). The final thing is that you don't want to have the cheese sitting on the bottom of the box. I have boxes that have slotted boxes as inserts and that works really well. However, it's pretty common to use a small stainless steel rack in the bottom. You can also cut a bamboo mat to size and put it in the bottom, but it is harder to disinfect (I use them sometimes and steam them in a large pot. This seems to work well. I have gotten infections that were obviously from the mat before, though, so be careful). In a pinch, I have even seen people just line up some stainless steel or bamboo skewers along the bottom and rest the cheese on that.
