I have always used PayPal for my online purchases and since I buy and sell a lot of sporting equipment and cards on EBAY it works well. You can link Paypal to a credit card and a bank account and pick your method for each purchase although one will be the default.
I have never had a billing problem with Paypal and their dispute resolution department has served me well and the few occaions when something went wrong, usually a shipment that didn't arrive from a seller. They are owned by EBAY and thus have to work well to allow all those transactions.