Your best bet is to choose a platform and include a Navio2 inside.
It will allows you to have a fully functional flight controller based on ArduPilot (same as PixHawk etc) and be on the Raspberry Pi hardware.
@dgaultie Welcome to the RobotShop Community. To expand on the previous reply, you might take a look at the following tutorial series:
None of the current quadcopters which RobotShop carries incorporate a Raspberry Pi compatible flight controller or mounting, so a bit of customization might be needed. The Navio is indeed the best option for a custom build.
You can find a variety of quadcopter frames in the category below. Some include more parts than others (frame / motors / electronics etc.) to the tutorial above should help you ensure that you have all of the parts you need to become flight worthy. https://www.robotshop.com/en/quadcopters.html