Videomaker – Learn video production and editing, camera reviews › Forums › Cameras and Camcorders › DSLR’s › Good video lens for a GH3? › Hi – as recommended above,
Hi – as recommended above, the $1399 Panasonic 35-100 f2.8 is probably your best bet. If you want to save a little money, you can get one for $1316 used at Amazon Warehouse Deals or new for $1201 from Japan through Amazon.
If you're shooting from the audience, you shouldn't need anything wider than 35mm. If you do, you may have to settle for a low light prime such as the $569 25mm f1.4, since the $1139 12-35mm constant f2.8 will take you well over your $3K budget, once the price of the GH3 is added in (even if you order the direct from Japan version of the lens for $1000).
Cheers and good luck with your project!