Define and give examples for "Bitcoin client" please. You mean like Coinbase? What about
https://blockchain.info/? If so what is considered the "safest" one these days?
I already have a BTC-e account and BTC deposit address so I'm good there
Coinbase AFAIK, does not allow direct import of private keys. Blockchain.info is very inconsistent and you are risking your BTC if you're going to use it. Electrum as they said are relatively safe but I would go for mycelium and use the cold storage spending feature, if you have IOS or android. Mycelium also support BIP38 decryption.
BTW, those saying electrum, does it allow the scanning of QR code?