MIgration of websites written w/ Joomla

I have a client that has a website built in Joomla. It uses several plug-ins, including MightySites, YooTheme Pro, ChronoForms 6, and Widget Kit. There is also an E-commerce component. Previously, the site was hosted with a virtual machine (running Linux) and using Vitualmin/Webmin control panel.

The scope of work is to migrate the site to a new host, using the most sensible method.