Bitcoin can only be sent/received from a wallet like Coinbase - so you'll absolutely need one of those. Setup a Coinbase account, buy the Bitcoin you want, then deposit from your Coinbase wallet into your desired site. Once you withdraw from that site it'll go back into your Coinbase wallet. You can then withdraw those funds back to your bank/paypal or use them to deposit from your wallet into another site.
Haven't had any trouble with my own Coinbase to date. If that's something you're worried about then you may want to look for a wallet overseas. Just do your research before setting up a wallet and make sure they have a good reputation.