The cost of an exam can vary a lot, I have heard ranges from $25 to $100, around here it is about $80. That is just for the exam, the total bill can be more for other services like a nail trim. A nail trim can cost $10-20. It can be good to see the nail trim done, and then do it yourself after.
The vet should be a full physical exam. This will include looking in the eyes, ears, nose, and mouth, taking the temperature and weight, listening to the heart and lungs, and feeling the whole body. They can also stretch out the limbs to see range of motion, look at the feet, and just otherwise looking over the whole rabbit. If you have any concerns about the rabbit, they can be looked at too. The sex can also be checked.
As for questions, you do want to make sure you are going to a rabbit savvy vet. The are lists of questions to ask before you book anything, then some to ask when you are there.
You should bring your rabbit in a carrier. Most vets don't like animals just on your lap since there would be other animals in the clinic and some might not like rabbits. A carrier is safest. Put a small towel inside and some hay in the back. A small dish for water can be good too, but bring some water and give it at the vet.
