Goodreader is a very good app, though I have to admit I use it mostly for file management myself. Apple's iBooks seems to be pretty good at managing pdf files, if you don't need to annotate them. But if you want to import all your 2200 books, you'll need to organize them in folders I suppose, and GoodReader would be better for that.
To get books into iBooks, you have to use iTunes I think, the simplest way is to add them to your books in iTunes and synchronize them. GoodReader has more options, though I don't think you can download directly from Google Books. Dropbox is the easiest way to get files on the iPad, many apps support it, including GoodReader.