There are a number of options of where to keep your EON.

In the exchange.
In an EON account

The second is preferred for storage.
The default wallet is the official Channels App by Exscudo, for iOS and Android.

For those that are not comfortable with handset wallets, there are other options to have a wallet on a desktop environment.

It allows all operations (color coins, multisig etc) but you will be dealing with a command line tool.

Eon Client https://testnet.eontechnology.org/client/

Community (3rd party) Desktop Wallet application for Windows. Utilises the API and provides a desktop interface.

Go to MyEonWallet

Testnet resources and basic client instruction :
https://eontechnology.org/testnet.html

Testnet Registration : https://testnet.eontechnology.org/

How to connect to EON testnet (Exscudo magazine) :
https://blog.exscudo.com/exscudo/how-to-connect-to-the-eon-blockchain-testnet-comprehensive-instruction/

Trevor Laird's walkthru videos for Eon Client setup & usage :