Amazon only sell Kindle books, these do not work on the eReader.
B&N is a site that I've never used before; they seem to make it very difficult to find out which format their ebooks in. They do offer the 'eReader' software for download, but this probably means it's in that eReader secure format, which IS NOT supported on the Sony.
With those two as the biggest stores, if you're set on using 'em, you may want to consider their own offering; it's just likely that you'll then have to get most of your books from their respective stores.
For the Sony, I haven't used the Sony store, but www.booksonboard.com
for my 'main' purchases, and I've just started to get into places like Smashwords for amateur \ self published stuff.
There's also some library services around the world that use a system called 'Overdrive' that allows you to borrow Sony-supported files for 14-30 days like a normal library book loan; make a start on finding libraries here: http://www.overdrive.com/
- and let us know the one you use, 'cos I'm sure all the ones aren't on there...