The official Ethereum site lists up a couple of wallet options for "storing" your ETH. It's a mix of different platforms, exchange wallets.
But to make things short, cryptoN00b recommends to start with MyEtherWallet, a client-side wallet MEW wallet that is available for mobile (Android and iOS). Once you got that installed and up and running with a wallet address, you can access your wallet also on desktop by visiting the website and connecting via MEWconnect and the mobile app MEW wallet, which is pretty cool.
On the desktop wallet you can swap tokens and buy ETH directly with credit card, deploy smart contracts, earn interest and check out some Dapps.
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