Localbitcoins
Coinbase
Bitstamp
Everyone recommends Coinbase
Coinbase is reputable to me. But I'd move all the coins off my online wallet.
Yes, definitely don't leave large amounts of BTC on online wallets. Move huge chunks to your offline or paper wallet.
Don't think you can use Credit/Debit Cards for LocalBitcoins or Bitstamp though.
You can't use credit card/debit cards directly on localbitcoins, but you can use Paypal or Skrill which both can be loaded with your credit cards. But it is much better to use Coinbase and Circile, as it is very difficult for you to find a trade with Paypal and Skrill on localbitcoins.