Using WP alongside another php script

Hello, I have a php script for a website which I have purchased ready to go (including css) but would like to incorporate it into a wordpress/buddypress blog with a theme from WPMUdev. Should I incorporate the purchased script into WP or incorporate WP into the purchased script?

Now, I’m not sure how best to go about this – do I run the php site from my WP blog using something like php-exec plugin?

Or is it better to create a sub directory on my domain which runs the purchased php scripted site and install a WP blog on the sub directory? If so, how are the two linked together? Ideally I want my WP theme to be the same throughout. Hope I’m making sense here.

any help much appreciated.