Web video is capable of streaming anything from 240p to 4k resolution.
Obviously, the higher the resolution the better it will look, especially when it's blown up to fill the whole computer screen.
240p will look very pixelated in full screen mode whereas 4K will look amazing. Ideally, look for a camera that shoots in either 1280 x 720 or 1920 x 1080. What camera to buy for web video: Anything that shoots 1280 x 720 HD resolution or better, preferably 1920 x 1080.
Examples of what to buy: iPhone 6 or similar, Canon 60D (or any DSLR that shoots HD video), Canon VIXIA HF R52 camcorder, Sony a5100 Mirrorless Camera, Canon XA20 Semi-Pro Video Camera (great for run & gun shooting), Sony AX100 (entry level 4K camcorder).