Using iPad 1st gen to read PDF files offline
You don't need to install any app from the App Store to read PDF files. The stock iBooks app is sufficient to store and read PDF files in offline mode.

You get the PDF files in iBooks, you can open the PDF file in Safari (if it is hosted on a web-server and accessible by a URL) and copy it to iBooks app. Alternatively, you can sync PDF files from your Mac via iTunes.

The iBooks app for iOS is no longer compatible with iOS 5.1.1 and it is no longer possible to install it on iPad 1st generation.

An alternate approach to get PDFs onto the iPad to read in offline mode is to iMessage it to the device. Step by step instructions as follows:


Set up iMessage on the iPad (by logging in with an Apple ID).
From another iOS/macOS device, iMessage the PDF file to the Apple ID setup on the iPad.
Once the message is received on the iPad, tap on the PDF thumbnail to download it. The PDF files gets downloaded and stored internally in the iMessage app. The same can now be accessed even without network.
To view the PDF, simply tap on the thumbnail to view it full screen.


The only glitch with this approach is that the last read page history is not preserved between launches. Neither are features like bookmarks and search available.