I got a website on which I want to sell a few services for which customers can sign up for and pay. It isn't a traditional ecommerce store and I only got two products. Does anyone know of a Wordpress plugin software that I can integrate into the site using shortcodes?
You can try this one
but I do not have any ideas about api (shortcodes) that will comply with this plugin
It seems, you are looking for a Membership Plugin rather then a full-fledged ecomemrce plugin. Take a look at s2Member or Wishlist Pro plugin for this purpose.