With motion, you're not always going to be able to control the subject's movements, and you won't necessarily be able to recompose as you would with stills. Therefore, the minimum focusing distance and hyperfocal distance of a lens will matter quite a bit more with motion. You want a close working distance for detail and macro shots, as well as separation of nearby foreground elements from the background, and you also want a good hyperfocal distance when choosing aperture for covering any play as subjects move through the plane of acceptable sharpness. You can't go wrong with image stabilization in a lens, either. Image stabilization eats up a bit more of the battery life of your camera, but otherwise there are few disadvantages to employing a lens with optical image stabilization, especially when working with literal moving pictures.
The Micro Four Thirds system mount that several Olympus and Panasonic cameras sport promises a much longer focal-length reach thanks to the 2.0x crop factor of the sensor, as well as much smaller form factors thanks to a shorter flange distance from the lens mount to the sensor. Olympus produces several popular mirrorless cameras with 1080p capabilities in the PEN and OM-D series, including the E-M5, E-PM2 and E-PL5. Panasonic produces the extremely popular Lumix DMC-GH2 camera and its successor, the GH3, as well as several other DSLRs and even a large-sensor camcorder, the AG-AF100, which combines the imaging quality of larger DSLR sensors with Micro Four Thirds-mount lenses. Micro Four Thirds lenses can be used interchangeably between the systems. There are several primes available to work with across the board, but keep in mind that each lens has a 2.0x 35mm equivalence value, so the Olympus M.ZUIKO DIGITAL ED 12mm ƒ/2.0, for example, is actually equivalent to a 24mm, which is the widest non-fisheye currently available. There's also the Panasonic LUMIX G 14mm ƒ/2.5 ASPH pancake wide-angle lens, the Olympus M.ZUIKO DIGITAL 17mm ƒ/2.8, the LUMIX G 20mm ƒ/1.7 ASPH, the fast 50mm-equivalent Leica DG SUMMILUX 25mm ƒ/1.4 ASPH, the Olympus M.ZUIKO DIGITAL 45mm ƒ/1.8 and the telephoto Olympus M.ZUIKO DIGITAL ED 75mm ƒ/1.8 with 150mm equivalence. Particularly useful for video, there are also two manual-focus lenses with insanely fast apertures from Cosina's Voigtländer line, the NOKTON 17.5mm ƒ/0.95 and NOKTON 25mm ƒ/0.95, while Tokina offers the 600mm-equivalent Reflex 300mm ƒ/6.3 MF Macro lens at a body size of only 66mm in length. There are also several adapters for using Carl Zeiss, Voigtländer, and Leica R and M mount glass.
A basic set across all formats should be able to cover wide, intermediate (50mm is a good starter) and telephoto fields of view. Often, these three key primes accompanied by a good standard zoom will cover the majority of situations whether shooting motion or still. A single prime set actually can give you twice the versatility in focal lengths if choosing to use both an APS-C and full-frame camera body, which is an option with both Canon and Nikon DSLRs. Thanks to the crop factor, a moderately wide 35mm on a full frame approximates a normalized 52mm to 56mm field of view on an APS-C camera, for example, while a 300mm would yield 450mm to 480mm approximately.
Sony currently offers two distinct lens-mount systems with video recording in the Alpha lines, the Sony A-mount for full-frame and APS-C lenses and the E-mount with APS-C equivalence for Sony's NEX mirrorless cameras and its line of large-sensor, interchangeable-lens camcorders. First introduced with the NEX-3 and NEX-5, the 1.5x crop E-mount system is relatively new, so there's a somewhat limited selection of glass with primes, including the 50mm ƒ/1.8 (so a 75mm equivalent), 30mm ƒ/3.5 macro, 35mm ƒ/1.8, 24mm ƒ/1.8 and 16mm ƒ/2.8 for a wide 24mm equivalence. The 10-18mm ƒ/4 zoom is also very wide. Sony's Alpha line has had a lot more time to mature, however, and there are adapters for using Alpha-mount lenses on E-mount NEX cameras and camcorders. Alpha-mount prime options include the incredibly affordable DT series of non-full-frame lenses like the DT 50mm ƒ/1.8, DT 35mm ƒ/1.8 and DT 30mm ƒ/2.8 macro. For both full-frame and APS-C use, there are also several available primes, including the 20mm ƒ/2.8, 24mm ƒ/2.0, 35mm ƒ/1.4, 50mm ƒ/1.4, 50mm ƒ/2.8 macro, 50mm ƒ/1.8, 85mm ƒ/2.8, 85mm ƒ/1.4, 100mm ƒ/2.8 macro, 135mm ƒ/1.8, 300mm ƒ/2.8 and 500mm ƒ/4.0 supertelephoto. Sony originally bought the A-mount from Minolta, so Minolta's A-mount lenses are also compatible.