It would like to know exactly what your hosting provider
said. I am interested in the provision of the required elements to run stack and I pay around $US11 a month for hosting that provides everything necessary for me to run it for experimental purposes.
Assuming you have a reasonable budget the problem for you is not getting the hosting or the software but the expertise to configure and maintain it. So that would require someone familiar with the LAMP
stack (the stuff that runs any interactive web site), and also to understand and deal with docker/ and the maxima stuff Tim refers to and how that ties to Moodle.
I am not a Mathematician but I have been looking at STACK on and off for many years and it is clearly an awesomely powerful tool. What stage are you at in working with STACK, have you tried it at all?