Can someone recommend a lightweight, but powerful, PHP framework that I can build a custom web hosting control panel on?
I have looked at CodeIgniter3, but is that a good choice?
Well I would suggest to use Symfony2 which is really great. It's not really the simplest framework but it will be very performant. Another good point in Symfony2 is the integration. You can integrate other existing Symfony2 applications in your own application (e.g. CMS, Wikis, etc.). This will reduce the development work you'll have to do on your own.