When painting a fireplace surround you should paint the fireplace surround using paint that is a heat resistant interior paint and the paint should be able to withstand temperatures of up to 200 F so that the heat generated by the fireplace doesn't start peeling the paint away.
Any interior paint will work to paint the fireplace as long as the interior paint is heat resistant to at least 200 F.
I would personally use Rust Oleum brand heat resistant paint and brush it on with a paint roller for best results.