The most popular way to process payments online is with Paypal.  I've been with Paypal for over 5 years now.  When selling online its important to offer options like Paypal especially when it comes to sites like Ebay.  You could be reducing your sales when you don't provide your customers multi options for payment.  Paypal is easy to set up and get going, even offering shopping carts, it is also easily integrated into numbers of scripts.

My other payment processing method I use is 2Checkout.com  They have proved to be a reliable source for making online sales.  They differ from Paypal because they are counted as the retailer and there is a $35 fee to set up and account.  

If you need to set up a ecommerce site from a database try oscommerce which is an Open Source ecommerce program.  All you need is a database and hosting.  Load you products into the database.  Setup your online payment processing within the site.  One of the easiest efficient ways to get selling right away.