You can download books directly from Amazon, B&N and iTunes directly to the iPad... no computer needed for that.
Just remember that if you aren't backing your iPad up to a computer regularly, if something happens to the iPad, you lose EVERYTHING!!!
It doesn't have to back up to a Mac, you know. You can put iTunes on any PC and back up. I had my first iPad long before my first Mac.
You cannot download the ibook app or the kindle app to the ipad2. Both require the operating system of the 3rd gen ipad. I tried to no avail. It makes no sense that you can't buy books for an ipad2 but if you can I have not figured out what I'm missing.