I think that registry office and courthouse weddings are the same thing here. I could be wrong, but I've never heard of anyone getting married in a courthouse here.
We got married in a registry office in a small village in Derbyshire. We had 50 guests with us. The guests were escorted into the room (the majority of them had to stand!), whilst DH and I verified who we were and paid for the certificate. Then the lady who married us went into the room, and we entered together when she announced us. I did not want to "walk down the aisle" by myself or be escorted by my father. I liked that we came into the room together, symbolizing that we were making this decision together. We got to pick our vows and were also asked if we wanted to use our own music, etc.
All in all, I really loved our ceremony. I'm sure that it varies from place to place. Since we got married in a tiny village, we were the only wedding that whole week, and maybe they were more flexible because of that.
Good luck with the planning!