Why can't I update my iPad to iOS 6 or 7? This is my first iPad, I can't figure this out - when I go to settings>general>software update I get "iOS 5.1.1 Your software is up to date"

I have iOS 5.1.1, also I have ubuntu on my PC (I see some advice about using iTunes, but I don't have OS X or Windows on my PC)
Which version of the iPad do you have? Not every version is compatible with every version of iOS; in particular, the first-generation iPad cannot be upgraded to iOS 6+. If that's what you've got, 5.1.1 is the latest version your device supports.

See this table on EveryMac for details of which versions are compatible with which operating systems.