Hard sided carriers are best. They protect in an accident or even if you stop suddenly, as well as not being easy to chew. They are also easy to clean and disinfect if needed. One with a top door is ideal, but ones that are easy to take apart are also good and tend to be cheaper.
Most of my carriers are like this. They are easy to take apart and put together again. They are also widely available, most pet stores carry them and others stores like Walmart have them as well. You can usually find them used as well, so that can make it cheaper.
This kind has a door in the top, but is also easy to take apart. It can be a bit more expensive though.
I would not recommend going too big. The small size will work for most rabbits and give them enough room to move around. Larger rabbits or pairs may need a larger size. A larger carrier does mean there is more room for them to move around, but also more space to be thrown around in an accident. For a vet visit, they arne't apt to be moving around too much anyway.
Some carriers will come with a pad or something to put in, but most do not. You can buy pads that are made to fit more carriers, but a small towel or fleece will work just as well. You should have something so they don't slide around and so it absrobs any urine. A handful of hay in the back gives them something to munch on. A small dish for water is good, but most rabbits won't drink, it is good to have for longer trips and just in case. Some carries come with a small dish.