When you download via Safari all it does is open the document in Quick View. It is not actually saved anywhere. To save the document you'll need to install a PDF reader app. There are plenty. If all you want to do is read them, iBooks is fine. If you want more flexibility try Goodreader or PDF Expert.
Once you have a compatible app installed you can tap and hold the open file in Safari to get the Open In... Options. Your compatible app will be listed as an option, and that is where your file will be stored.
Goodreader has a built in browser so that you can go to sites and download files directly to it. It is worth getting for a variety of other reasons as well.