No advice from me about circumcision, though I would ask for SOME type of anesthetic- that's just gotta hurt!!
Eye care- they ask if you want it delayed because a baby's eyesight is pretty clear and they can focus for a short period of time immediately after birth. This is important bonding time for you and your baby as your baby takes in the "blueprint" of your face and connects it to your voice. The eyecare that they are talking about are drops/ointment they put in the baby's eyes to prevent infection (infection can come from things such as a bowel movement you have during delivery or STDs that you may have, etc.)
Generally you should be able to hold, nurse, or "bond" with your baby for up to an hour immediately after the birth. They will usually take the baby, weigh him, do a quick checkover, and wipe him off so he is a bit easier to hold and check for abnormalities (but most times they can do all of this in the room with you.)
After your time with the baby, they will probably take him to the nursery to be checked over by a dr and bathed, have a blood test, footprinted, etc.
Be sure to ask your dr or midwife any questions you may have and call the hospital too- they should be happy to give you specifics and you can find out if they honor certain requests you may have for your birth.
Congratulations!!
-Amanda