There's only one coin you can store in your MyEtherWallet and that is Ethereum. The others are called tokens. Tokens relies on a coin's network. To be clear, cryptocurrencies that relies on a coin's blockchain is called tokens. ERC20 compliant tokens are the other "coins" you are talking about. MEW can store all the tokens as long as they are Ethereum-based tokens.

MEW is a secure wallet. You control your assets since you have your private key. Just be careful. There are many phishing sites out there that will try to snatch your private key. If ever you wallet is compromised, it will always be your fault and not your wallet's.