It depends on what cryptocurrency you want to purchase. Omisego isn't listed by all the exchanges, so I purchased some Ethereum from Bittylicious (or you could use Coinbase as @jamesgw200 does) , sent it to Bitfinex where I traded it for Omisego, then sent the Omisego tokens to MyEtherWallet. You could leave the currency you buy in the exchange, but if something should happen, such as the exchange getting "hacked" all your money is gone.Which exchanges have people used then for transfer “coins”