The iPad allows you to buy books from several sources, not like your Sony which limited the format you could use.
iBooks for Apple books, and any non-DRM epub
kindle app for Kindle books (you can buy directly from the iPad, and transfer)
Kobo app for epubs from Kobe (may work with your Sony books, not sure)
goodreader app for PDF or Word doc books
eReader app for books from Fictionwise or ereader.com (can buy from iPad)
Barnes and Noble app for Nook books
All the apps are free, and with the exception of Goodreader all will allow you to buy or transfer directly from your iPad. Goodreader uses drag and drop from within iTunes, or cloud apps like dropbox.
I am not sure about your Sony books though. I had a Sony reader (sold it when I got the iPad) and know their DRM is Adobe Digital Editions. Kobo uses the same DRM, so if there was a way to get the books into Kobo App it might work. I remove the DRM from all my books, so it was not an issue for me.
Hope that helps