The two easiest gateway APIs I have used are authorize.net and paypal. The biggest difference is cost and feature set between the two. Paypal has no recurring fee services that take a percentage of each charge while authorize.net (as far as I know since it has been years) has recurring charges as well as a percentage of each charge. Either way the site could accept credit cards or checks. Using paypal you send the user through a paypal page and using authorize.net you construct the page.
PHP works well with a number of DBs though MySQL is the most common.
If the client already has a gateway account try to find out if they provide an API for PHP or SOAP/XML-RPC.