Let's say I'm making a site similar to e-bay (connecting buyers and sellers). Which payment provider should I use as of today?
If you're considering adding off-site payment methods, consider how you are going to integrate these with your web analytics package - at the very least you are going to need to be able to tie the payment back to the originating session, so that you can incoming links (especially paid links) to revenue.
If the off-site payment process has more than a single page, have each step of the process tracked within your analytics package if at all possible. It's really helpful to be able to track how far along the payment process your users are reaching before bailing, to work out if there are UX problems preventing your users from giving you money.