The reason why Coinbase is considered “unsafe” is because of incidents like the MtGox hack that resulted in everyone losing there BTC. Centralization has its issues.
If you want to move to a wallet you control, I would highly recommend. It’s a chrome extension that creates a lightweight wallet with client side encryption. No one can ever see your private key but you. In addition, you can browse and participate in Dapps.
If you want an even higher level of control, you can use MyEtherWallet, a client side wallet generator that is the gold standard of personal wallets. You can generate a public key, move your wallet into cold storage and move on.
Originally posted through Quora.