I think a better answer is a combination of the two answers above.
The paper wallet is what you need, and the ONLY thing that you need.
As long as you have a working version of Armory on some PC, this is true. It doesn't even need to be online, or be compatible with any version of Bitcoin Core. As tspacepilot goes on to say:
Make sure you know how to export your private key and address from armory into some sort of plain text. As long as you can do this, you will not have a problem long term.
And as long as you have a working version of Armory, you can do this. You need to do a Wallet Restore using your paper backup, and then go to the Backup Wallet option and choose "Export Key Lists" as your backup type. This will produce a text file, and although you may need to change the formatting of the text file a little bit to get it to import into another wallet client, it shouldn't be too difficult.
It should be noted that you can't export the entire wallet and expect some other wallet client to be able to generate addresses/keys the same way that Armory currently does, instead you have to ask Armory to generate a list of addresses and keys as described above, and import the entire list into the new wallet client.