If the pet is ill, neutering should wait until the animal is healthy. The exception would be if the dog/cat is already under anesthesia (i.e. cleaning up wounds after a dog or cat fight) -- then it is usually OK to neuter, assuming that the dog/cat is not in critical shock. Antibiotics will most likely be given, depending on the case specifics.
If the animal is having another elective procedure that requires antibiotics, such as a dental cleaning in an older animal, it would be OK to neuter if the veterinarian gives the pet a clean bill of health overall, rather than have two separate anesthesia sessions.
On a related note, post-operative pain medications are given by many vets these days and are a good idea for pain management and keeping the animal quiet during the recovery period. The post-operative medications will vary, based on the procedure, the animal, the primary anesthesia used, and each veterinarian's preferences. Some anesthetics last longer than others. Ask your vet if you have questions about your pet's post-operative pain management.
