What should be kept in mind while buying a video camera?
Depends on the use and budget, but my list starts with: 1) Get the largest lens diameter you can afford - with the largest imaging chip system available, preferably 3CCD or 3CMOS. 2) In addition to "auto" modes, the following manual controls need to be available - on the outside of the camcorder: Focus Shutter speed iris/aperture white balance audio gain (stereo) video gain 3) There must be a video-out connection to connect to an external monitor that can show the video being captured. 4) Headphone connection to monitor the audio being captured. 5) LANC connection. 6) Dual memory card slots. 7) XLR audio inputs (1 for left side and 1 for right side audio channels.) 8) At least 1 accessory shoe. Two are really useful. Other features should come along with the above: Optical image stabilization, (minimum) 20x optical zoom, lens hood, built-in mic mount, zebra control, built-in neutral density filter settings, a good selection of frame rates, resolutions on compression methods. I currently use a Sony HDR-AX2000 and Sony PXW-Z150. I am saving up for a Sony PXW-Z190 (the Z280 is a little too expensive for my video hobby). For an action cam, I prefer the narrow profile of the Sony Action cams - and one of these days I will replace my Sony HDR-AS30V with the 4k version. Panasonic and Canon have some competitive equivalents, but over the years, I ended up with Sony gear and their NP-series batteries work well with third party accessories like on-camera or (some) stand-mounted lighting. The Hero series can get fine video, but their wide profile is not useful to me.
What you intend to do with it.
Size, storage capacity, battery life, video quality
Thanks, @Bela for the suggestion. Do you take any extra care for the video to be more stable with your phone?
Make sure it has video stabilizer on it
It depends on what it's being used for, but I would make sure that it's better than my iPhone. I have an iPhoneX. I already have a video camera worth several hundred dollars capable of recording in 720p and 1080p embedded into my iPhoneXS that I spent almost $1,000 on. It seems that this should go without saying, but I'm saying it anyway because I read an article leading up to Christmas about how so many people buy video cameras for hundreds of dollars thinking that it will of course be far better than the one they or whomever they're getting it for have in their phone only to find out it's no better than and often actually inferior to the camera they have in their phone. There may be a need for a camera that's better than your phone, but before I went down the road of buying a separate camera, I would see if I can get that need met by upgrading my phone first. Since cameras are in phones, you're duplicating a lot of the cost of a phone buying a camera, so to be worth it, it should be far better than anything you can presently get in a phone. If not, you might find it better to just upgrade your phone to the one that can meet your camera needs and sell your existing equipment to offset the cost.