Hi Susan,
If you have a laptop computer, there are several seats that are allocated for laptop users (a few in the west search room and some in the upstairs south search room).
I would also try, if possible, to book a seat at one of the downstairs search rooms (East, West, Dome). The South Search room is no different, but involves an awful lot of walking up and down stairs if you need to get a microfiche copy of a record that is not clear on screen etc. You can book a seat in advance by phone for no extra cost.
Also, as you will be paying £17 for a day pass, remember that time is money, so it might be worth bringing a packed lunch - there is a room set aside for those wishing to eat, and probably a better option than looking outside for somewhere to eat, as there is nowhere decent close to hand.
I would bring a to do list, as Lesley says, and you might want to bring a handbook with you listing parishes and counties with the relevant Chapman codes etc - I have my Kathleen Cory book to hand all the time, as well as a road atlas if I need to look up an obscure placename! The info is available on site if you need it, but it wastes valuable time having to leave your seat to find it.
You will find pre-1855 Church of Scotland OPRs, post 1855 BDM and census records all digitised and available from your seat. Some OPRs also list mort cloth records (for burials), and there is a folder just off the Dome area which lists what records exist on site for which parish. Mort cloth records have not yet been indexed or made available digitally at each computer terminal, so if you want to search these, you will have to spool through microfilm in the Dome search room.
If you have any families from the dissenting churches (those that broke away from the established church), or Roman Catholic ancestors, use the National Archives of Scotland wesbite's online catalogue to establish what is held there prior to your trip - it is next door to the GRO, and if you know the records are available there, you could possibly factor that in to your day if you need to. (NAS has free entry). (Typically the dissenter churches will be those such as the Free Presbyterian, the United Presbyterian Church, the Secession Church, etc).
If you want to try and narrow down searches for the children of a particular couple, there is a disc based version of the IGI available for consultation in the Dome as well which could get you started quickly, though you could also do this at home using the online IGI before travelling to Edinburgh. Don't assume that if you have found something on the IGI that you will find it at the GROS, as the IGI is often innaccurate. Often the GROs will hold additional records to those you have found on the IGI - I've often found seven or eight kids when the IGI has only listed two or three!
Above all else, don't be afraid to ask one of the staff for advice or help at any stage - that is why they are there!
Good luck with your search - and enjoy the thrill of the hunt! lol
Chris