Which credit card processor is right for you really depends on your specific needs. We generally don't recommend one over the other. That said, PayPal Payments Standard (aka Checkout Express) and Stripe are relatively easy to get started and don't charge a setup fee or monthly minimum, whereas Authorize.net and Paypal Payflow are both more involved and require a merchant account. Also, please note that Stripe is only available for businesses in the United States, Canada and United Kingdom.
Links to more info on each option are below:
With "Paypal Checkout Express", you can actually use any of Paypal's core products, as summarized at https://www.paypal.com/webapps/mpp/compare-business-products
(Please note that when signing up for a Paypal Payflow account, your email address used on that account will need to match the email address with which you log into Full Slate.)