Hello,
VirtueMart is an open source shopping cart solution that integrates with Joomla!.
Joomla and VirtueMart are written in PHP and can be used in typical PHP/MySQL environments.
Please share the more details as I am expert in using the API as well as virtuemart expert.
I am available now to discuss about this project with you, please message me for the more details.
Thanks,
Anil