Coinbase offers the cheapest methods, but you don't have as many payment methods to choose from as you do with LocalBitcoins. Coinbase is a business, so you're buying coins from a business. It is also centralized. LocalBitcoins, on the other hand, is peer-to-peer, like Craigslist and decentralized.
Coinbase supports bank transfers, credit cards, debit cards and bank wires. If you want to buy Bitcoin with anything else you should go with LocalBitcoins.
Each method of deposit on Coinbase is relatively easy and straightforward.
If you want to deposit through your bank account, first you need to select the bank:
Then you will be prompted with a login screen to verify your bank account.
You will need to provide:
1) Your online banking username
2) your password
This is a one-time verification step. Once your bank account has been verified, Coinbase claims the logs are deleted. If you're uncomfortable sharing this information you can use the deposit verification process that generally takes about 2-3 days.
If you use a credit or debit card you can add these as payment methods to your account by visiting the payment methods page.You can also add funds in a similar way with a wire transfer.
While you can't use Paypal to buy or deposit funds, you can use it to sell Bitcoin or withdraw funds. Go to https://www.coinbase.com/trade, select 'Sell', then select 'PayPal account' as the Payout Method.