MyEtherWallet is safe to use yes.

When you make a wallet on there you get your own address and get your own private key.

The private key is used to access your funds. Watch out for other websites that try to look like MyEtherWallet. Some websites have a very similar name like MyEtlerWallet or MyEtherWalet or whatever. They will steal your funds if you accidentally go to their site and put in your private key.

Additionally, you can have a backup made and import your MyEtherWallet into any other ETH wallet if you want to. Though you need to be careful as not all wallets support ERC20 tokens. My Ether Wallet supports all ERC20 tokens.

Make sure you keep backups of your private key. Keep a written or printed copy in a safe.