I recommend offering a variety of payment gateways (if you can) as then people can pick the method of payment they prefer...
PayPal = Integration (Positive), Flexibility (Positive), Cart Support (Positive), Recognition (Positive), Dispute handling (Negative).
Google = Integration (Average), Flexibility (Positive), Cart Support (Positive), Recognition (Average), Dispute handling (Average).
Amazon = Integration (Average), Flexibility (Average), Cart Support (Average), Recognition (Average), Dispute handling (Positive).
PayPal is well recognised, highly supported, has the best API of them all but unfortunately their pretty bad in cases of payment disputes.
Google is pretty good on the recognition, cart support, and dispute handling support but their API isn't nearly as good as PayPal's.
Amazon are the best for handling disputes with payments but their pretty average in most other respects, the flexibility included.