You don't need a merchant account until you have a really high volume of transactions. Instead you can use a 3rd party payment processor. There are lots of popular ones like:
As far as the shopping cart goes you have lots of open source programs to choose from. Which one you go with depends on how much information you want to collect. Most of these programs are designed for physical goods so they collect the usual name, address, shipping info. If you need to collect more information from customers you may have to customize the shopping cart or look for an extension/plugin that allows you to do that. Anyway you can start with opencart:
: selling services with opencart. note the bit about disabling shipping.
You need not worry about the software having more features than you need. It's all free so you use what you need to and ignore the rest.
BTW if you are using drupal as a CMS for the rest of the site you can try ubercart. Wordpress also has a shopping cart plugin called getshopped. The advantage of using these is that they will integrate well with the rest of your site if you are already using these CMS.