I use a hardware wallet(keepkey), electrum and blockchain.info sometimes.
Don't keep the bitcoins online at exchanges like OP said, it's really not safe.
I want to try those hardware wallets, but I don't have enough extra money for that. I think that's better compared to having an old laptop to be your cold storage, it's portable, and it's easier to use. Keeping it on online exchanges can expose your bitcoins for attacks.