Separate PHP app: inherit styling from theme?

Hi — setting up a replacement for a hand-coded website. I’ve got WP going fine, I’m using Canvas (with a view to adding WooCommerce someday.)

Part of the original website is a single monolithic PHP application, written in roughly 1873. (Okay, I exaggerate, but not much: it’s a MySQL backed PHP state machine, in one monster page, mostly pre-CSS.) Someday, I’d like to re-write it completely: shift to WP’s login mechanisms, etc. That’s not today.

I’m looking for a good starting point to get the PHP app to pick up the theme styling. I’m not sure if I am better off just hand styling it, or embedding the app within a WP page (can I do that?), or trying to pick up the theme’s CSS…

Thanks.

–LairdB