I notice that with animations, some will load first, then play, others play fully and smoothly without issue, and some will play partially, stop to load more, then play, then stop and so on until fully loaded. Is the reason the source of the video, or something to do with my browser (Chrome)? It's really disruptive to watching said videos, and I can't find any way to make them either load first then play, or load smoothly all the time, sometimes making a short video take a comparably long time to play back fully. Any ideas on how to fix this issue?

Download the video in its entirety and view it then. Otherwise, view it from the source which may have faster servers (whenever applicable).