I wonder which method of accepting online payments is best to use on your site. paypal shopping cart to accept CC payment or 2checkout system or your own merchandise account?
Well it depends on your location. If you are United States than any Payment processor is best for you. In India we have only PayPal who can provide better services.
It depends on the volume you are doing too. If you're taking in enough payments it is worth getting set up with a real credit card processor. You might look at some of the shopping cart programs to make sure they will interface with whatever you decide on too.
I've always used paypal, I don't care much for their fees, but its widely accepted and the average person that uses the internet has atleast heard of paypal.
You can have both Paypal and 2CheckOut. There are some countries where they are not being serviced by Paypal but they have credit cards so they can 2ChecOut to pay for any service or goods you may offer.