Pick a Camera
Cameras should be lightweight, and ideally have a dimension which lends itself to convenient mounting. Drag is more likely to affect vehicle performance than weight, so it is often wise to pay a mass premium to save on drag.
The team has used several cameras before.
H107 X4 Camera: Purchase
480p. Lightest and smallest camera, no shell, very delicate.
Mobius Action Camera: Purchase
1080p. Light, robust, small, remote startable, live video out.
808 Camera: Purchase
Resolution is hit or miss, different batches have different resolutions. Cheap, but sketchy. Avoid some version numbers. See this page for more details.
Sony Action Camera: Purchase
Expensive, but good. Live video out. Records telemetry that can be overlaid on video.
Mount Camera
The rocket team used additively manufactured camera aeroshells on Project Therion.
Project Odyssey also included an internally mounted camera. It malfunctioned.
Pitfalls
Many cameras have serious thermal issues. These issues are compounded when the form factor is reduced. Mobius cameras in particular will shut down due to overheating. Most western launch sites will be well above the working temperature for all the cameras listed above.