The fees on all Bitcoin you buy with a credit card or PayPal will be through the roof if you're not willing to verify your identity to an exchange - you can do transactions with PayPal or credit card on LocalBitcoins, but people will find it very hard to trust you since both choices (especially PayPal) are reversible, which is also why the fees are so high.
There's Coinbase, but you will have to verify ID - same goes for other reputable exchanges. If you're only looking for a small amount, Blockchain has a credit card option from your wallet which doesn't require ID and CoinMama also does up to $150 worth I think. For large amounts it's probably not worth the effort.
Once you have a Bitcoin wallet, you use a traditional payment method such as credit card, bank transfer (ACH), or debit card to buy Bitcoins on a Bitcoin exchange (example: Coinbase). The Bitcoins are then transferred to your wallet.It is best to transfer your Bitcoins to a secure wallet.
