There are all sorts of tools for going handheld with motion. Rigs like the models from Redrock Micro are highly modular and let you put the camera into a variety of positions. To keep the camera steady as you move with it, a counterweighted rig like those made by Steadicam and Glidecam are excellent options with a lightweight camera like your regular mirrorless or DSLR body.
Lenses For Motion
Your regular still photography lenses can do a great job, up to a point. One of the biggest advantages of true movie lenses is that, in a given series, all of the models will have the same size lens barrels and controls will be in the same place so you can swap lenses and not have to make any adjustments for focus pulling, etc. The Zeiss CP.2 primes, Rokinon and Samyang cine lenses, as well as the Tokina Cinema ATX zooms are good examples of popular motion-capture models.
Aerial drones are moving from the RC hobby arena to the photography and videography mainstream. Commercial and movie productions have been using large octocopters to carry small movie cameras for years. Now much smaller quadcopters like the DJI Phantom 2 Vision+ and 3D Robotics Iris+ place HD cameras on drones that can be carried in a backpack. The DJI Inspire 1 was introduced in late 2014 and shown at CES where its integrated 4K camera created a considerable buzz. Aerial videography remains complex and it takes a lot of practice, but these well-integrated solutions make it possible to master their use without having to solder circuit boards and control wires. The view from above is fantastic, but where drones can really create some amazing footage is by using them for tracking shots. See Philip Bloom’s short film Koh Yao Noi for a great example of this kind of shot. Find it on his site, philipbloom.net, or go to Vimeo and search for it there.