I do not see problem with using caching plugin with Appdev. The Extinct theme preview site (uses a similar framework) in fact is hosted on a cached server while due to some issue with style switcher(which should not concern buyers since it is used for demo preview site only), I could not enable the caching in time for Appdev.
As far as minify is concerned, I cannot guarantee that things will work fine since I have had people report haphazard ordering of CSS files by the plugin when minifying making the priority of styles to change and hence the theme to take a different look and feel. Most JS files have been pushed to the footer and hence I am not sure it’s very beneficial to minify them other than reducing the number of HTTP requests. May be there are options in the Minify plugin to control the ordering of files included and if so, you can consider its use. Let me know if you find out something and need help.