Here's the Beginner's guide to buying a camera for video
Resolution
The most quoted video specification you'll see for a camera is the output resolution, typically 1080p/Full HD, 4K or even 8K on the latest cameras. Most recent TVs can display 1080p/Full HD, and the ability to show 4K video, which has twice the resolution, is becoming increasingly common. Shooting 4K footage gives some flexibility during the editing process, even if your final output will be 1080 whereas with 8K capture: it affords you some creative flexibility (in terms of cropping or stabilizing your footage) if you're outputting a 4K video. The file size has to be lot larger and require more storage accordingly.
Frame Rate
Most video is shot at approximately 24 frames per second or 30 frames per second (with 25 fps being the standard for TV broadcast outside North America). But many cameras offer faster frame rates, which can be used in a number of ways. 60p footage can do a better job of representing motion, so can be a good way of capturing bursts of action. The alternative is to capture 60p or faster and then slow it down to 24 or 30p, to give a slow-motion effect. Most cameras can't offer fast frame rates at their highest resolution, but 1080 capture at 120 fps or faster is not uncommon, which can be great if your project doesn't have to be 4K.
Recording limits
Another detail to check is whether a camera has any recording restrictions. Some models can only record for 29 minutes and 59 seconds (an old restriction that related to import duty), but most end up being limited simply because high-resolution video capture generates a lot of heat. Pro video cameras have cooling fans but most stills/video hybrids simply try to transfer this heat to the camera's body panels, where it can escape into the environment. The best of these designs can continue shooting for extended periods, while other models let you disable their overheat limits
Audio
A microphone input socket is a must: the internal microphones in cameras tend to be simple affairs that will pick up ever movement of the operators hands or clothes moving nearby, so you'll want to be able to attach an external microphone
Autofocus
One of the biggest distinctions in modern cameras is how reliably their autofocus works when capturing video. Unlike stills shooting, video captures all of the camera's attempts to focus, as well as the moments it's in focus, so you'll need a camera that's decisive and dependable if you're hoping to trust it to autofocus while you're recording.
Focus peaking and Zebras
The alternative to autofocus is, as you might expect, to focus manually. This is the way a lot of professional video is still shot. Most modern cameras let you use autofocus to set your initial focus position, before you start recording, then provide a 'focus peaking' function that highlights the edges of the in-focus points in your scene. When used with an appropriate lens (ideally one with linear focus response, where the focus always changes by the same amount as you turn the focus ring) and a bit of practice, manual focus is pretty workable, but a lot of subjects can be arranged so that you don't need to re-focus very often.
Settings carry-over
One detail that won't be mentioned on a camera makers' website is whether exposure and other settings are carried over from stills to video shooting. The ideal photo settings are often drastically different from the ideal video settings, so we prefer when exposure, white balance and focus modes are kept separate.
Image stabilization
Stabilization is an essential part of video. At its most basic this can mean the use of a tripod with a head designed to move smoothly for video. Cameras with in-body stabilization can allow greater freedom of motion, letting you add some dynamism to your projects.
High Dynamic Range capture
Unhelpfully, the term 'High Dynamic Range' is used to refer to two things: modes that try to squeeze a wide range of bright and dark tones into standard footage, and modes that capture a wide range of bright and dark tones for playback on HDR TVs that can properly display them as bright and dark.
Log capture
The other type of video that benefits from 10-bit capture is Log recording: a way of capturing and retaining more information about the original scene, to provide greater flexibility when you come to edit the footage. Log footage tends to look very low contrast and desaturated, to prevent color or tonal data clipping and becoming harder to edit.
Raw output
Some cameras can capture or output Raw footage, often requiring an external recorder to encode the results into a quasi-standard format. In principle this gives a level of control over the brightness and white balance of the footage, beyond what's possible with well-shot Log footage.
Getting the most out of your video camera
Whatever camera you choose, the ability to shoot and edit high resolution video can be an exciting creative adventure. There's a lot to learn, even if you're familiar with photography, but the satisfaction of capturing and creating video footage can be immense. There are extensive resources on the internet to help you as you learn, and with the latest models, it won't be your equipment holding you back.