You should do the most safe way, buy Bitcoin and deposit that to your exchange account (ex. bittrex, binance, poloniex) and use that to buy other cryptocurrencies. If you want to hold it then transfer it to more safer wallet. Of course the safest way to secure your coins is to store it on a hardware wallet but the problem is not all cryptocurrencies are supported by them, so you will have to find the official wallet for that specific altcoin or you can just use a multi asset wallet like coinomi, exodus, or jaxx. It also gives you your private key so it is safe. Most people sell their altcoins by converting it to Bitcoin because it is more easier to find trusted exchanger for Bitcoin to fiat currency. But if you can use coinbase you can use it also to sell Ethereum, Bitcoin Cash, Litecoin.