More great advise as always Monica.
Personally I would opt for the SP Centre in Edinburgh as its £10 for the full day compared to £14 for Park Circus (So thats £4 towards the train fare), Its directly across the road from Waverly Station so easier to get to, and most of the records are there so they will get you any which are hard to read on the screen.
They also run a free 2 hour taster sessions throughout the day for anyone who hasn't been before to assist in how and what you can find.
Although there are plenty of seats I would advise phoning and booking a seat in advance. I've been several times over the past month and found the staff very helpful.
Oh and last point............. There's also a cafe for that well earned cuppa coffee.
More details can be found at -
http://scotlandspeoplehub.gov.uk/Gerry